Regeneration has lost all significance and wonder and magic and bittersweetness that it once had. It used to be that the Doctor regenerated only when he was finally defeated in some way or if he had to make a final act of sacrifice. It represented the end of a character we had grown to love and admire even if we often disliked him at first. As much as I initially disliked and prejudged each new Doctor, I grew to love and lament the loss of each of them from Hartnell to Tennant. That was the magic of regeneration. Now it's a plot device, drained of all emotional impact and meaning.
This is one of the things that has bothered me about the show as of late, and you've hit the nail right square on the head. Regeneration didn't used to be something that was brought up or bandied about every other episode; as you said, it occurred when the Doctor was basically out of options, and we always knew that he was burning through them a mite faster than the average Time-Lord.
Now, he's apparently got 9-10 more regen cycles, depending on just how many River has actually used on herself at this point? I guess that solves the question of how to keep the show going once Smith leaves and we would've eventually approached that (originally) 12th and final regen.
But this whole issue really does sum up just how drastically the show has change even since RTD left, let alone it's how different is has become from the source material.