Fully agree with this. Look at the legacy of Halo for Xbox. I knew people that sold their PS3s to play Halo. If Sony is going to go big on GAAS they need their premiere game to be fully exclusive. But this is a good management approach since you a) need to develop a good game people want to play and b) you have to identify it as such to market/release it correctly.The logic doesn't make as much sense as you think it does.
An exclusive live service game would be *more* of a draw to The Playstation Ecosystem because it's pulling in networks of people who want to play together. Imagine if Minecraft actually was an Xbox exclusive. You don't think that would drive Xbox sales. It would be a much bigger draw than Starfield.
The reality is ALL AAA games are extremely expensive to make. All games need to reach the biggest audience. Everyone more readily accepts/expects live service games to be multiplatform because they're often free/cheap and the publishers are extremely nervous about that.