oh definitely. Games just felt differently back then. It was rarer for games to hold your hand, too. Not to say that that was always a good thing, sometimes it was quite annoying I guess, but maybe it was part of the reason games felt different. Combined with having to find stuff out on your own, you literally were on your own, yeah.
There are many things though that make this era of gaming special, this one is just something I often think of.
Oh that sucks. I only had this problem with a Dualshock 1 a while ago, my Dualshock 2s thankfully never got into that state. Maybe it has something to do with how they're stored? Anyway, you can always replace the thumbsticks if cleaning doesn't help.