Yes this is a significant hammer blow against native apps on iOS, but I don't think this would reduce cost for the consumer. I might be misunderstanding what you mean by "freely accessible" though. Definitely is more convenient for the same web app to be available everywhere.
Freely accessible as in not vetted by Apple. No approval process, no need to pay $100/year, no need to buy a Mac. (Also, gone would be the 30% Apple tax on "in-app" payments.)
You'll need an app-specific cryptographic key to connect to the push service, unless that's changed. And you'll need some system for registering and de-registering push tokens (unless that's also changed).
Yes this is a significant hammer blow against native apps on iOS, but I don't think this would reduce cost for the consumer. I might be misunderstanding what you mean by "freely accessible" though. Definitely is more convenient for the same web app to be available everywhere.