Because once their servers go dead they're little more than fancy coasters.
Take for example, MAG, the multiplayer-only, PS3-exclusive developed by Zipper Interactive / SCEA.
It only had a lifespan from January 2010 - January 2014. Now you are literally unable to play it.
Why the hell would I want to have games in my collection that act as ticking time bombs subject to the whims of the developers?
I want to take control of MY game. I want to own MY game. I want to play MY GAME 20 years from now. Shutting down the game the instant it becomes unprofitable? Hell no!
That's why I like games with single-player components...so there's something left after the community dies out.