I can see why people wouldn't want River now "trapped" in that computer forever. But I just look on it as it being a program of River's memories, not actually her soul. So, she's not really trapped, her experiences are merely archived.

In a way, I can see why the Doctor would consider this a good thing, because it's apparently very similar to what his own people do on death, downloading their memories to the panatropic net.

So, to him, it was the culturally "right" thing to do.