Any website implementing a form for data entry is expected by any sane user to autofocus the first form element.
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.
Your original comment was to use tabindex to skip search, menu bars, breadcrumbs, etc. and for that there are better options.