please. build for people, not validators. it's good to check for mistakes, but validators are far from a stamp of approval for anything. know what you're doing instead of seeking 'validated' crap.
People generally don't read HTML... machines do; the further levels of validation you can obtain (and certainly to the extent to which the code is somewhat valid at all, such as making certain to have tags that aren't misusing quotation marks or brackets or entities), the more likely your code is to be understood in the same way by random implementations of HTML parsing that may be used in the field.
yeah, I remember injecting flash objects with javascript wrapped in cdata, so the w3c validator confirms my awesome coding skills in green, good times. now I treat validators as useful tools for double-checking syntax, and nothing else. it validates more often than not anyway, but it's not that I care.
invalid code doesn't mean shitty code, and the other way around - being valid doesn't say anything about the practical quality of code. know your craft = know the rules + know when you can break them.
Here's the thing: It's not uncommon to come across weird bugs/rendering errors on web pages that were caused by incorrect HTML (where the developer writes </a> where he should have written </p> and similar issues). Pages with those kind of errors might render fine in Browser X and yet have render errors in Browser Y. That's why you validate - to find those kind of bugs.
Unfortunately on the topic of accessibility you're likely going to need to design for people, but build your site to validate. I don't have much experience using screen readers, but from what I can tell they're going to need at minimum well build HTML.
Well, yes (build for people) and no (stuff should be technically correct, as well).
For instance, the WGAC 2.0 guidelines require that HTML be valid, and if a client wants WGAC 2.0 compliance (even A level, not AA), the site's gotta validate [1].
unless you are doing it for bureaucracy's sake (public sector, etc.), do what works, not what some ink on paper from half a decade ago says, otherwise it's CYAE[1].