Actually, gen xer, I have usually forgotten too--when I get the thank-you note later, I'm always going, "Hmmm, what shower did I go to recently? Oh, yeah, right!"
I don't actually sit around waiting for people to jump through hoops. But if you're going to send me a thank-you note, you'll get a better effect if you don't use stick-on labels for the addresses, and don't print out a very generic-looking note from the computer.
And I personally make sure to send them. Because I know that people *do* notice. My MIL has complained about having sent a present for the baptism of Niece's Baby No. 2 (she couldn't attend the event because one of my kids was having a first communion), and never having heard boo about it. It bothered her. She went to the trouble to be generous, and it wasn't even acknowledged. She wouldn't have gotten bent out of shape about a label, or typing, or a text, or a phone call.
But she remembered!
I also look at thank-you notes as a major PR opportunity! This is my chance to look so good in front of all these people that the NEXT time they have any reason to give me or mine a present, they'll remember how nice they felt when they got the thank-you from me.
And they'll be generous and happy when they select a present.
(The PR is not actually about getting more gifts, though; it's about them liking me so they give me the benefit of the doubt in the future if I do something wrong, or forget to write the note, etc.)