We will never see that, because were such games to be implemented, all that would happen would be a series of increasingly lopsided victories for the men in essentially every sport.

Let’s have a flick through various sports and see how men and women shaped up against eachother:

Football

• Just before the US women’s team won gold at the Olympics (they were already considered to be the best in the world), they lost 8–2 to the men’s under 17 team (and the USA men’s team is really quite poor).
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• Having won the world cup, they then promptly lost 5–2 to the Dallas under 15 men’s team
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• The Australian Women’s team (5th best in the world) lost 7–0 to the Newcastle Jets’ under 16 male team (Australia and men’s football really don’t go together FWIW).
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• Note also that the sides they lost to are not very good. Australia, the USA and MLS teams have not produced many if any good players.
• Take a peep at the men’s World Cup final/Champion’s League final, then look at the women’s (there are clips on youtube of both). The gulf in quality and endurance is pretty clear even to a casual observer.

Tennis

• Vjekoslav Nemec has already given a good answer with the time both Williams sisters were beaten on the same day by a journeyman tennis player: Vjekoslav Nemec's answer to How can I argue that boys aren’t necessarily better at sports than girls?
• The battle of the sexes that a film was made about included an ageing, overweight ex pro in his mid 50s against a woman on top of her game.
• Indeed, there is a reason that women’s tennis is best of 3 rather than 5 sets as the men’s is.

Athletics

• Here’s a list of the fastest 100 m times for men in the world. The fastest time is 9.58 seconds. The ‘slowest’ is 9.75 seconds.
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• Here’s a list of the fastest 100 m times for women in the world. The fastest time is 10.49 seconds. The ‘slowest’ is 10.71 seconds.
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• The fastest female time , if included in male rankings, would come in below at least 2600 faster men. The table stops at 2600, where the slowest man is Mike Rogers at 10:09.
• It is also worth noting that there are serious questions over whether the fastest woman (Florence Griffith-Joyner) used steroids - she mysteriously retired as soon as it was announced that random drug testing out of season would be introduced… Sure, in the top 10 men you will notice Gay, Blake, Powell and Gatlin, all of whom have doping history - but not only are there non-dopers like Bolt, but also if FGJ - even with steroids - could only come below 2600 men - that speaks volumes.
• Let’s have a look at the 100m finals at the 2016 Olympics. The maximum time to run the 100m that you could still qualify with was 10.16 for men and 11.32 for women - a huge difference.
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• In the final, the slowest man - Travyon Bromell - did it in 10.06 seconds with a strained Achilles’ tendon.
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  The fastest woman - Elaine Thompson - did it in 10.71 seconds.
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Rowing

Let’s look at two of the most popular races: the coxed eight and the coxless pair, at the Olympics.

The coxed eight:

• In the men’s coxed eight, the winners Great Britain finished in 5:29:63. The last placed Kiwis finished in 5:36:64.
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• The slowest qualifiers were the Poles in the repechage in 5:59:52.
• In the women’s coxed eight, the winners were the USA with 6:01:49 - slower than the slowest male qualifiers. The last placed Dutch finished in 6:08:37.
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How about the coxless pair?

• In the men’s coxless pair, the winners New Zealand finished in 6:59:71. The last placed Australians finished in 7:11:60.
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• The slowest qualifiers were the South Africans in 6:27:59, and the slowest non qualifiers were the Spaniards with 6:54:26.
• In the women’s coxless pair, the winners Great Britain finished in 7:18:28 - slower than the men who did not even qualify.
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Basketball

• WNBA teams practice against male players. As in, not NBA players, not college players either. This is college guys who couldn’t make the draft and couldn’t make Europe either, and high school players. The coaches often have to tell them to tone down their level of play so the training session is productive for the women.
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Ice Hockey

• The Canadian Women’s Olympic team - the best in the world at present, and gold medalists at every Olympics since 2002 - practices against 15–18 year old male players from Midget AAA teams. Even without contact rules, they seem decently matched.
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• Have a peep at the midget league rankings. The Canadian women’s team is ranked bottom, albeit since it has played half as many games.
• However, even if you double their points won to make up for half as many games, that puts them on 22 points - still 7th out of 9 teams.
• They have a 56% winning percentage. That puts them at joint 6th in the rankings.
• The USA Women’s Olympic team - at the time as silver medalists in Vancouver the second best team in the world - managed to lose to a boy’s high school team 6–3 in their warm up for the 2014 Winter Olympics in Sochi.
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Golf

• In 2003, Anika Sorenstam was one of - if not the - best female players in the world. She had already won 4 majors, and would subsequently win two more that year. She became the first woman to compete in a PGA tour event in the modern era. She competed in the Colonial National (now the Dean & Deluca tournament) - a tournament that is not particularly hardcore, and ranks 30th in prize money. She shot 5 over par, finished 96th out of 111 players, and missed the cut.
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• The 1998 Johnnie Walker Super Tour pitted male and female golfers against each other . The winner, Vijay Singh, finished an impressive 39 strokes in front of last placed Laura Davies, despite her being considered one of the best female players, with 4 majors under her belt as opposed to Singh’s 1.
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• Undeterred, Davies tried again in the 2004 Korean Open, where she missed the cut by 4 strokes.
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  She tried again that year at the ANZ Championship, again missing the cut, finishing 14 over par and beating only an injured player with back problems.
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• The best known player was of course teenage prodigy Michelle Wei, who tried 13 times, making the cut once at a low ranking tournament, almost making the cut at two PGA tournaments, and spectacularly failing against lower ranking male golfers for the other 10.
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• She most famously failed to make the cut for the 2004 Sony Open by just one stroke, and the 2005 John Deere Classic by two strokes. However, since that things went downhill, missing the cut in the same tournament by 14 shots in 2007.
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  She finished last at both the ’84 Lumbar Classic in 2006 (registering one sole Birdie) and the Omega European Masters.
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  At the Casio World Open, she beat only one other competitor (an amateur) by a single stroke, without a single birdie, and finished 27 strokes behind the winner.
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• She made only one cut in her entire career at a men’s tournament: at the low ranking and rain-shortened SK Telecom Open in Asia in 2006. Additionally, the Asian tour is considered less prestigious & less competitive than both the European and American tours. Her last appearance at a male tournament was the alternate event (low profile and sub-standard players) Reno-Tahoe Open in 2008. She missed the cut by 9 strokes.
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Before someone pops up in the comments and either accuses me of being misogynistic, or points out that any of those respective women’s teams would walk over me:

1. Whether a female team would beat amateurs is beside the point (although even at collegiate level, there is in my experience a marked difference). The point is that if you are comparing like with like, and elite men against elite women, there is a clear distinction - and even at a collegiate/high school level there are clear trends.
2. I am not suggesting that women should not play sport, or should only play some sports, or are inherently bad at sport. I am only pointing out that there is a notable difference in performance.

So yeah, it won’t make for a fair match of for interesting viewing.

Footnotes