As a general criticism to my pitch, I hear that history is not as enticing. PS1 games are fine, but hardly why everybody buys GP in droves - because that would be new first party games day 1.
Sonys current strategy is to maximise both the box office profit of traditional games sales and the revenue from subscribers/streaming service. They already have 50 million paying subscribers, but can also release a title that sells over 4 million copies in a week.
I believe that they will eventually transition over, as gaming as a whole becomes a service. When that happens, they will likely try to move the 47 million PS Plus subscribers over to PS Now, significantly invest in the service and put their first party titles on it day one.
PS Now, at the moment, is more of a secondary consideration, they're basically just investing in the infrastructure so they're not caught off guard with rapid changes in the market. Like wetting their toes.
To move early though and follow the exact same strategy as MS, they would likely lose out on billions in gaming revenue.