That is annoying, I don't want it on my home screen but it seems to be the only way to turn it into a 'native app'.
I don't think Progressive Web Apps are ready for the mainstream, but I'm hopeful that in the next few years we can get there.
Unfortunately it's a limitation of the Android platform; you can't add arbitrary launch activities at runtime. So the Chrome team is unable to fix this AFAIK.
However, you could imagine a future release of Android that sports a custom homescreen app that just includes Chrome progressive webapps in the main app drawer. Or someone might be able to write a third-party homescreen app already that does that. (Not sure if Chrome exports that data though TBH.)
Also, FWIW, the "add to homescreen" is really just icing on the cake - even without it, PWAs save data locally and are launchable offline. If you remove Pokedex.org from your homescreen, you'll notice you can still navigate to https://pokedex.org while in airplane mode, and Chrome still reports some 6MB of Pokémon data as being stored on your device. (It remains to be seen whether this is a bug or a feature... but we'll see how many PWAs abuse it.)
However, I have uninstalled the Facebook app from my phone, and now receive push notifications from the mobile website, which I have on my home screen. It's a fantastic experience.