I was always made to write thank you notes as a child...I hated it.
But clearly something has rubbed off as I now get my children to do them (albeit without quite the levels of neat handwriting/amount of newsy content I had to do).
And I do think it's rude not to thank people after the party, as in 99% of cases, presents are not opened at the party (in fact, I can't think of a single party where the child opened the presents there and then).
I am a bit judgey about this, and I'm not a fan of generic 'thank you for the present' notes as I think it's nice to know your present has been associated with you.
However, I'm realistic and having seen that most people don't write thank you notes at all, a generic note is better than nothing. I do notice when we don't get one at all, and I agree with people who say it makes you a bit less inclined to bother thinking about an appropriate gift in future.
Incidentally, I do hand write notes, I've never done them on the computer, even for whole class parties. If this makes me old fashioned so be it. I just feel bad until they are all done. And when we've been to a party, I often text to say thank you to the parents - particularly if it's someone we don't know well, ie you wouldn't necessarily expect to be invited.
I do think it's strange that there are whole swathes of people who never receive thank you notes of any sort - round here there's a definite mix of all approaches.