Asbeau: It's not laziness, it's convenience. Today's gamer doesn't want to manually download, patch, archive, and burn discs because they see no tangible benefit from the time they waste doing it. The world has moved on and your boxes of carefully hand-labelled silver discs are an anachronism, and your reasons for hanging on to them just sound like empty paranoia.
To me it depends what games we are talking about. Games that receive updates often and especially online multiplayer games which expect all players be on the same patch levels => yes please, auto-update my games.
But then when I think about many of my old PC retail games for which I have more problems finding patches nowadays, I kinda wish I would have gone through them earlier and downloaded all the latest patches manually, and not rely that "sure someone will keep them available online from here to eternity".
I was wishing patches-scrolls.de would be my go-to site for getting the updates for my old retail games, but for some reason I have trouble downloading anything from them anymore. Have their download servers gone offline? Also I am not quite sure if some updates they've had before have been removed...
That's also why I'm in the bandwagon of having backed up all my GOG games already now, instead of waiting if and when GOG will eventually go the way of DotEmu, Desura etc.
Since I have "only" a 10Mbit/s internet line, it is also about convenience for me for the bigger games. If I get an urge to try some bigger game quickly (say, Witcher 3), it is far faster for me to just install it from my external HDD, than downloading/installing it through a client. Having my own local collection of installers allows me to be more impulsive.
I guess people with 150Mbit/s couldn't care less, they download several gigabyte games in a matter of minutes I guess. For me it means extra hours of waiting, not very impulsive anymore. I kinda have that problem with many of my Steam games, I think "I wonder if I should try that game I have on Steam?", but then realize that since it is so big and I have to wait for it to download/install for several hours (or even the whole night), I just forget about the idea. Maybe later (or not)...