He does care because he wants stability for the NCR to be stable. People aren't going to be going to Vegas to gamble and have fun if they are busy fighting one another.
Courier: "Say you keep control of New Vegas. What happens next?"
House: "What is the NCR? A society of people desperate to experience comfort, ease, luxury... A society of customers. With all that money pouring in? Give me 20 years, and I'll reignite the high technology development sectors. 50 years, and I'll have people in orbit."
"Why would I want to go to war against the NCR? They're my best customers. If their leaders weren't scheming to steal Vegas out from under me, I'd have no troubles with the NCR at all."
So he not only likes the NCR, he is dependent on the NCR for his long term goals.
As for what factions would be in the NCR (Core Region) since Fallout 2... very few. Many such as the Khans, Vipers, Jackels and even the Followers have been driven out.
There is one interesting faction mentioned to be in the NCR and left alone, Ciphers but I don't think we need a game based around them.