The problem with D3 and Sim City isn't that they use DRM. The problem is that the servers were unable to cope with the number of players, so thousands of people who paid for the game were unable to play it.
Steam has millions of users playing DRM-ed games, who don't complain as long as there are no server outages.
For a decade before Steam, millions of gamers played games where the DRM system was entering a CD-Key printed on the disc/manual, and that was just normal.
Then there's a second issue, D3 doesn't just use DRM, but the game logic is hosted on a server. This isn't DRM, this is turning a single-player game into a server-hosted game. This caused anyone who wanted to play LAN games to legitimately complain, and people without fast internet to legitimately complain.
e.g. For me, the closes D3 server is across the entire pacific ocean, meaning that even when I play single-player, I have several hundred milliseconds of lag, which is enough to make the game's "hardcore mode" unplayable.
DRM makes sure that only authorized people get to play the game -- forced server-side-hosting of the game-logic makes sure that no-one gets to host a game, not even people who bought it. Under this system, the DRM makes sure that only authorized people can be clients of a game, and then the private server system makes sure that no-one but Blizzard can be a host of a game.