https://webkit.org/blog/3709/using-the-system-font-in-web-co...
...and even if you get pixel-perfect between android and ios, you sacrifice "cultural-correctness" (ie: floating buttons v. top bar v. bottom bar, etc.).
Writing two pixel+cultural perfect apps on two platforms, keeping them in sync, making sure they're not buggy, attempting to share code, attempting to keep them both secure is incredibly expensive. If you don't believe me then do it yourself.
Making a PWA which gets 90% of the way there, and integrates as well as possible with the system (ie: fonts, location, notifications, accelerometer, etc.) is generally _less_ expensive than doing a single native app well, and has the chance to get you 90% of the way there on desktop and your "alternate" mobile platform.
PWA can be incredibly powerful (along w/ manifest.json-style support as android has), and I'm waiting for the day apple catches up to android on this one.
I'm okay with them living in the browser and gaining the performance advantages, offline support and push notifications.
Nobody but designers who think too highly of themselves wants this. Everyone else wants the app to fit in with the platforms toolkit. This requires the designs to be different.
"Writing two pixel+cultural perfect apps on two platforms, keeping them in sync, making sure they're not buggy, attempting to share code, attempting to keep them both secure is incredibly expensive. If you don't believe me then do it yourself."
Which is why I don't do it the way you described. I embrace what makes each platform unique.