I'm a little afraid that putting PWAs in an app store
may actually reduce the flexibility they offer by
restricting what PWAs can and can't do
Not sure what you're saying here. Are you afraid that app store policies (privacy requirements etc) will be stricter than what you can do with browser APIs, or that the app store will ban API abuses that're currently necessary for acceptable performance/usability?
The web is analogous to an untamed forest. It's got a bit of everything in it, and you can choose which parts of the forest you wish to go to. Don't like app XYZ because it locks up your CPU? Don't visit its URL. If you like and trust app ABC, use it regularly. It's like when you visit a restaurant - if the food's good, you go back. Otherwise you don't. I feel people are smart enough to work this out on their own without needing a corporate app store to set out rules for everyone.
If we start to restrict the web, I feel it takes away from what makes it great; the fact that it's a platform for untamed creativity and choice.
