Hypothetically, if they'd wanted to go a totally different direction, the could have courted game developers willing to create games for them that would have been offerable at a pure-subscription rate. But they chased AAA games and hit a major market issue: there was no way AAA publishers were going to under-cut their per-unit sales in other channels by offering with-subscription access to their product and trusting Google would pay them enough to make that worth their while.

You didn't actually need both the subscription and the game. Subscription is just for > 1080p streaming and other 'pro' features. You could just buy a game without any subscription.

Stadia didn't require a subscription. You could just buy games and play them. But loads of people came to the conclusion that you needed a subscription. My going hypothesis is that this was caused by the free trial of the subscription service (higher resolution, cheaper games) that everybody got when they launched. So since people couldn't access the games without getting the free trial they assumed that this meant that they couldn't access the games without a subscription.