If the one getting its ass kicked makes those games more scarce on its competitor's console, it becomes more difficult for you, the consumer, to choose one, which means the market got more competitive.
Absolutely not. Splitting up the market between mutually exclusive options is not competition, it is cartel tactics. Competition doesn't happen only at the console-maker level, it involves all gaming companies.
Before if I wanted to play certain games I could choose to buy from ActiBlizz and Microsoft or ActiBlizz and Sony or ActiBlizz and Nintendo. Now I can only buy from Microsoft period. There aren't even more games. There is less choice, less competition.
You shouldn't get too comfortable with what Microsoft is doing this just because as a game company it's in third place. Don't forget that in size, overall, Microsoft is larger than Sony and Nintendo combined, several times. It's not even the first time they do it, they did it to Zenimax/Bethesda too.
Sure I do hope that other smaller publishers grow to take that space, but will that space even be available, considering your suggestion that people might choose to buy a XBox and play those same games?