It's not just funding. Apple changed webapps to delete indexedDB periodically even if they are inatalled on the home screen.
There's no way to have a great experience if you can't store data permanently.
Ask yourself the same question about Native Apps. Why should any Native App be allowed to store data permanently. The answer to that question is the same for Web Apps.
Web Apps can be every bit as capable as Native Apps except with security and privacy built in. For consumers, businesses and competition, Native Apps need to be relegated to to apps that require cutting edge use cases
Unless the app is open source why would it matter to me if it is build on free and open technology?
I would say per definition a webapp is less free than a native app as its under the control of the server operator and not running locally. I know iOS have somewhat webified apps to let them control if people can run them but the old idea of the native app would be entirely under the control of the user, even if its closed source.
I also dont think a web app can do privacy as well as a native app. A native app you can firewalled off from network access while with a web app you are at the mercy of the developer and server operator.
They'll make you submit your PWA for app store review, sign your asset and JS bundles so all other's won't load, make you support "Web IAP", and go through review again every time you want to update your bundle.
Hitching your "I want to be be free of Apple's platform control" to "I want PWA's" is a recipe for disappointment.