Re: "see the capability gap between native and web apps closed as much as possible"
PWAs don't have any less security that a standard web page run through chrome. You can put the same, or better controls in place and have a bit more control than many web pages.
As for PWA vs Native it's often a different use case and a decent PWA doesn't have to be 'janky and slow'.
Apps have passed their peak for most people. When smartphones first came out many people were searching APP review sites, waiting for app of the day recommendations. Reading every update note for every app to see what amazing new features it had. Doesn't happen anymore. People don't search for apps randomly, it is based on a real user need and most people would prefer not to download a full blown native app just to get information when staying at a hotel, or pay for their pizza etc.
Combine that with the fact that you can have a website (lets say for a theme park) with fully up to date information, shopping carts, pricing, calendars etc. You then get a native app built (perhaps two if you want to utilise all the features of IOS and Android and don't want to restrict yourself to Xamarin or the like). Now you add a major new feature to you responsive web page and you might have to get the apps re-written and accepted onto the app stores. If your new functionality actually breaks the old functionality you risk any users of the old app or the period where it is getting published not working and have to try to carefully sync between website and apps.
If it was a PWA run off the main site the changes by the web developer could instantly and automatically 'update' the PWA. Always the same code, always in sync, nearly always the same bugs to fix. The same backlog, same developers and project team.
Absolutely won't suit all app use case but that doesn't mean they aren't much better for some use cases (and a short term app when you are visiting somewhere would be a good use case).
It reminds me of the days of the web where a parts catalogue supplier would require you to download a piece of software to see their catalogue, nowadays you just have the parts catalogue and checkout on their website. No one would download a piece of software just to browse part (or book a holiday, or get driving directions), but they would download program to play a modern game.