heyo: I apologize for the lateness of my reply.

The player with more points (on the board) has more opportunities to place stones in his own territory than the player with less points, so he should win the game anyhow.

That may be true, but it changes the strategy of the game. You would have to switch from surrounding territory to trying not to play the last stone, and then you're not really playing Go anymore.

First, as I already mentioned, white may have fewer points on the board but may be leading by komi

That doesn't matter. If white has fewer points on the board but leads by komi, then he wins. Period. That's how the komi rule works.

Second: the player with more groups is in a disadvantage because he has maintain 2 liberties (eyes) for every group.

That's a good point. If players are forced to move, they may be forced to fill in their own eyes, and that would change the status of the game.