1. Lack of support on iOS. I presume it’ll stay this way for a while (years!). Mobile Safari finally has service workers, but really, that’s about it. No support for “Add to Home Screen” (technically it’s there, but doesn’t work the way it does in other browsers), and a lot of other APIs.
2. The Web is missing some APIs that would really let it compete with native apps. I know there was WebNFC at some point, but it was dropped. No standard/widely implemented API for reading contacts, sending texts, etc. Features like that would really push PWA over the edge and make it awesome.