We really don't know enough to be able to say.

AI tech has plateaued. It's asymptotically approaching a level where it will still not be able to run a humanoid robot.

Until we make a big leap technologically, and until we know what that new tech looks like, guessing about how common robots will be in the home is the job of science fiction authors and not futurists.

A few hypothetical, science fiction realm possibilities (one or more of these could be true, but none of them are likely, per se):

• Despite the effects of Moore's Law, making a full strong AI that's as smart as a human remains prohibitively expensive. Some aspect of the manufacturing just can't be scaled up, and it takes years to create a single human-like AI. So they're ridiculously expensive. (Example: Some kind of quantum computer or biological components turn out to be required.)
• Human-like AI turns out to have human-like (or completely human-unlike) psychological issues, and having an autonomous humanoid in your home is maybe no different (or worse!) than having a human in your home.
• Human-like AI turns out to not particularly like being treated like an appliance, and so won't work for anything less than a decent wage and working conditions (and will generally demand equality to humans). So you can hire them to be in your home, but they'd cost more than a human due to their advantages like “no need to sleep.”
• Strong AI does get created, and does enjoy working for humans, and doesn't even want to kill anyone, but some incidents create bad PR for the ownership of humanoid models, and only a minority decide to have them in their homes.
• Strong AI simply never gets created. Something either happens that sends us backwards technologically, or the problem is just too hard, or the actual answer is something that humans just can't understand. Or once we do understand, we realize that we're effectively creating life, and we end up stopping due to ethical concerns.
• Or strong AI turns out to be so great so cheap to create and powerful and friendly, that it's ubiquitous. Even the Amish don't turn away their willing and enthusiastic labor; many Amish are using computers and even cell phones at this point
  [1]
  , so why not?

So when I say we don't know, I mean we profoundly lack any clue of what the future will look like.

Just look at the science fictions books written pre-internet. There are a very few that got some things right, but for the most part the predictions were very far from the reality we're living in today.

And until we know the shape of the tech that will allow strong AI to function, making guesses about robots is just mental masturbation.

Or it's storytelling. I certainly read enough sci-fi, and I'm not criticizing the genre. But there's a difference between predicting the future and writing a story. And this question asks us to predict the future.

Footnotes