> web apps are clunkier and provide a worse experience because they are not well supported by the OS

No, they are clunkier and provide a worse experience, because most "web apps" are ported version of desktop bloatware, targeting devices, permanently plugged into wall-mounted electric outlet.

What are "web applications" anyway? Something, that requires permanent internet connectivity? Something with DOM APIs? Something with built-in Javascript interpreter? Something with CSS support? The defining qualities of "web" have absolutely nothing to do with mobile devices. If anything, "web" has bad supported for OS. This is why all hybrid frameworks are about exposing additional OS functionality to browser, not the other way around.

Just accept, that you are looking at wrong tool for the job.