I think probably YANBU but that not all of what you said is true.
Just answering for the independent school I work in:
smaller class sizes
Yes - but this does also mean our classrooms are correspondingly smaller. And also we have chosen to use our small size to allow us to make half key stage bubbles rather than year bubbles to enable us to fulfil more of our normal curriculum. We could have chosen to use the small size to allow for greater safety instead but we haven't.
larger premises
To an extent, yes. We are quite a small school but have a lot of space, especially outdoor space. I think that's more because we're rural than because we're private though. Many urban private schools are tiny.
more money for sanitiser and cleaning, handwashing facilities
Yes. We've just had wall mounted hand sanitisers put in every classroom and children are going to have to use them on the way in and out of every class. We don't have endless money though so we haven't built extra toilets/sinks.
many have put in place safety measures. Sanitiser, optional masks, one way systems, staggered lunch time, optional use of masks, testing
Only sanitiser from your list. We have 2 lunch sittings already but haven't gone further than this. In this way I think state schools are safer as many have said children must eat packed lunches in their classrooms. Our parents pay for lunch as part of the fees and wouldn't be happy with children eating in the same room they have lessons in so that wasn't an option for us.
parental expectation
YES!! This is the big one. We charged about 90% fees last term. Parents won't stand for that again. We did give full, interactive online education, clubs, assemblies etc for that but it was still so substitute and parents know that. We will do everything possible not to close this term.
they can set their own rules and make parents sign up
I don't think so?? We still have to follow the guidance. A lot of the guidance is terribly woolly though so schools can vary a lot.
can insist on temperature checks
I suppose we could. Not currently in the plans though.
richer parents more likely to have holidayed etc
Not sure about this, tbh. Most of our parents are only richer than the average state school parents before paying school fees. After paying them they are often significantly cash poorer. The most common holiday destinations for our pupils are Cornwall and Norfolk. There are the very rich who are often on exotic holidays around the world but that wasn't possible for anyone this year. I don't think our parents are any more likely to have been to Spain/Italy/France etc than any other parents.