Is there any possible way for the NCR to win in the end? Or do you really have to stick with Yes Man and make New Vegas a independent place?

I only completed the game once and couldn't really find a option that lets the NCR rule the wasteland instead

Don't tell me that the only way to win is to get rid of the Legion/NCR or kill them?

Yes, there is a way. Pay attention when you reach the strip, you're given the quest hook shortly after you show up.

Yes Aliasnear - pretend you hate robots (despise them) and don't even speak with them when dealing with Benny.
As mentioned, the NCR will quickly reach out to you...
L8R

You can also let House and the Legion win.