I think the acquisition was meant to improve that situation directly. Software sells hardware, not the other way around.
Brand, popularity, history of the brand, history of the popularity, mostly sell hardware. Software alone wont sell hardware.
Lets say that 10 million gamers bought super popular game 123, 3 million on xbox, 7 million on playstation. Now sequel 1234 comes only for xbox, does it sell 3m + then make 7 million playstation gamers buy xbox? no.
Because xbox is failed as global brand, unpopular, unwanted and is seen as "not cool option" in big parts of the world
So buying software and make it exclusive doesnt add up into 1:1 amount of PlayStation users getting xbox. Maybe at USA where xbox is their competitor, but not globally. I would guess that maybe 1/100 playstation gamers are willing to get xbox if they would not get bethesda games anymore. so maybe 1 million sold consoles. MS is so rich that they dont have to care, they can buy devs and spam money without losing in big scale.
Xbox have long road ahead to become anywhere near as popular as PlayStation.
Just look at this current gen launch, PS5 sold out everywhere for months and months to come, while it have been possible to walk into a store and buy xbox series s since the launch (on many eu countries at least), and even series x were available for weeks when preorders opened + some where available on launch on stores, even when rumours tell that they had less consoles to sell.
It is huge difference to sell out for +6 months vs being off the shelf product. Even switch cant compete with PlayStation on many areas, switch never sold out here, even on launch. Yet even ps4 have been sold out or hard to find around xmas every year.
If MS buys tons of devs and makes games exclusives, they just gain lot of haters whom just stop buying those games because they are pissed at their strategy.
Because it is obvious that if company rather "steals" games from gamers, rather than building new IPs = company is not likable.
Kind of like when movie makers replace old character with different ethnicity/gender to gain some stupid political correctness points, many people dont like it (at least outside of US) because it is obvious that makers & crybabies are too lazy to make new good characters so they must steal old ones and replace it to gain some agenda.
Same with games, remove old IPs from all gamers, trying to push people to their ecosystem = they will gain haters, not new users