The idea that any franchise can be turned into live service is some really Pollyanna type thinking.
Blablabla. Come back when you get actual arguments and not "it's obvious" bullshit.
God of War could be turned into a GaaS game but it wouldn't be God of War. Even with the 2018 reboot, God of War isn't the same God of War from the mid 2000s. It would be God of War in name only. That you list a bunch of games and don't inherently understand why they work as live service is pretty telling.
I don't hate GaaS though it's not for me personally. I've said this for years. Nor did I say Sony should stop making them.
It's not for you means you know nothing about them, how they work, how they operate, how franchises transformed into gaas. But still sprouting bullshit based on what, voices in your head? Typical armchair analyst - zero experience, full confidence.
Unlike you I play gaas all the way since 98' and played a lot of them, going as far as designing/developing one (small MUD for like 200 people, but still), so I know a little bit about them.
And who the fuck cares about live service be a "God of War" you considered proper? World of Warcraft is not Warcraft 4, still it's a great game and excellent addition to Warcraft universe.
Industry doesn't care about narrow-minded fanatics like you, and players often like expansion of their franchise even if genre or representation is changed. GoW18 also follow this routine even if you are unhappy that it's not a follow-up GoW4.
And no, it's not just name. The reason why established franchised on the level of God of War are easier to convert to gaas than make a completely new franchise from the ground is that established franchise already has a world players know with it's lore, NPC, events etc. So players get into familiar environment, it's easier to attract and retain players this way. And yes - it's you who know nothing about why this or that live service successful or not, you have zero practical experience, all you have is wild delusions "I know it better"
Sony felt like they could just take their current studio model and adapt it to live service, but it doesn't work like that. It's worked for games like MLB and Gran Turismo, so I don't blame them necessarily, but in the grand scheme of things the result is failure.
They have plenty of franchises that could work as live service, but they need to know how to present it and they need to know how to support it.
Sony wouldn't know what to do with Fortnite or Roblox.
In grand scheme of things we have exactly one failure and one success. Yes, idiots try to overblow failure, but it doesn't change the score.
And Sony themselves treat it as it is - 1 success and 1 failure and resolute to continue with live service games, ignoring the rabid fanboys and their forum whining
As for would Sony know what to do with Fortnite or Roblox... Sony DO have one of the most successful f2p game of all times and they manage it just fine (unfortunately it's already archaic, but still very active, and not scalable to other projects). So much knowledge of f2p games.