My take is that they’ll go exclusive as much as they can because they’ll take a short term hit on copies sold if it slowly strangles the competition. Your right there not out to hurt Sony, but they’ll do it if it means they grow.
They want people to get on board with Xbox or more key, gamepass and if a big exclusive gets someone to dip in then there all the more likely to stay. This doubles down if the next big exclusive is again an xbox exclusive.
I disagree with your point that smaller titles like Doom will sell systems. I honestly think the “masses” will just not play them if there not available on their chosen platform. What I do think they do is inform your choice of platform and keep you there between the tentpoles and they look even more attractive to the casual if there “free” with your subscription.