Do most students just let their offers expire on May 2nd?
It is not required but is considered good form to notify a school that you will not be attending. Some schools give you a way to decline (ex. portal, postcard) or you can send a quick email to admissions. It is quick to do and would reflect well on you and your HS. You can decline an acceptance at the deadline or whenever you are 100% certain you will not be attending the school.
Yes, it seems like the polite thing to do, considering there are students on waiting lists and such 
It is helpful to your peers and to schools that have offered you admission to let a school know you will not be attending as soon as you are sure.
Do schools who admit 5,000 students really notice which kids decl one vs. letting expire? And do they start processing the waitlist before May 1?
You never know what the future might bring. You might want to transfer to one of those schools in the future. You should politely decline by the decision date.
A few schools start processing their waitlists early for various reasons. If their yield is running behind the usual levels by a certain date. Or they find out something that allows them to add to the freshman class unexpectedly.
My daughter has been politely informing her “non-choices” that she will not be attending. At least for two of them she was offered a merit based scholarship, which they can now offer to someone else (I am pretty sure that universities over-book on admission, but I am not sure that they do in offering scholarships). It costs us nothing, takes very little time, and maybe somewhere there is a very happy kid or two.
Yeah, you should politely send an email to notify the school you are not coming. While you may not be going there, it may be someone’s dream school, and it allows the college to have a good idea of their wait list which could really help someone out. It is just the right thing to do.
One school that my D did not notify them her declination, they contacted her to verify even that was a pretty prestigious school.