In the short term it’s not a problem, but when you look at it in the long run, you end up with a game that has limited lifetime. Not because the game stops to work, but because of it’s reliance on a big enough player-base. So you can’t really go back to these games, maybe to play a round or two with some friends.
A good example might be Battlefield. Battlefield2 is still pretty fun in LAN mode, because you can fill the game with bots giving you the proper battlefield experience. But in Battlefield 3 you just end up on a dead and empty server.
Another example that comes to mind would be Strike Vector. I’ve always wanted to play the game, but I’ve never bought it, because the player base died before I even got around to even thinking about buying it.
The Unreal Tournament series would be a example of a game series with great AI. All UT games actually had a relatively large offline-only player base and can still be played solo or with just a hand full of friends.