I would be very surprised if a website autofocused almost anything on page load, except for very specific applications where that makes sense. I just tried clicking through some forms on gov.uk, which is a website that has spent a _lot_ of time testing and improving the UX of their forms, and none of them had autofocused elements, not even on later pages after having already filled in elements.
I can imagine screen readers would deal particularly poorly with this behaviour, because the user would be dropped in a field without any of the context of the page, just the field label to work with. However, I've not been able to test that out properly.
I don't think the behaviour you're describing is anywhere near as common as you think it is, and I suspect it would make a page less accessible for a number of kinds of users.