The way Apple implemented Home-Screen Web Apps was by placing a thin wrapper around a UIWebView.
Hence, Home-Screen Web Apps are not like Mobile Safari at all in actual implementation.
They are, instead, exactly like an iOS application developed by a third party developer who put a thin wrapper around a UIWebView.
Hence, they do not get the same special privileges as Safari Mobile.
That is a fact of their implementation.
The alternative appears to be that to create Web.app they went to all the trouble of reusing the Mobile Safari code, and then methodically went through and broke things such that it behaves exactly like every other application that uses UIWebView.
This would seem like an unreasonable way to get an application that behaves exactly like an application that uses UIWebView.
It makes a heap of assumptions though, and feels kind of like a non-techie person saying "why dont you just whip up a GUI app to trace my IP". Enabling Nitro JIT for UIWebView for some applications without enabling it for every app in the app store is probably more difficult than toggling a switch.