To be fair, this is happening to all media, not just games.
But in my case, really the opposite is true - it's my digital media that I feel like I can own forever, not the physical stuff. I mean, right now I've got so many Xbox 360 games cluttering up my closet. Eventually I will have to go through them and either sell or throw away most of them. I am never going to play them again and they are wasting space. Also, my Xbox 360 itself has started to crap out - half the time I have to use a butter knife to open the damn disk tray.
Meanwhile, I've got games on my Steam account that date back to the mid-nineties. I don't have to worry about those.
Yeah, I get it, Steam might disappear tomorrow and everything could be lost. But the risk of a provider going down, compared to the risk of physical stuff breaking or just winding up in the trash, feels pretty inconsequential to me.