I've tried fullscreen web apps before and it didn't work for me. A simple use case to illustrate where it failed in terms of UX:
- User clicks the "Forgot password" button and gets a password reset link to his mailbox. Clicks the link and hey, the reset password page is now opened in a new tab in Safari. Fullscreen experience ruined.
This also applies to things like logging in with your Facebook/Google/etc account, purchasing things (think Stripe).
Note: I'm talking iPhone here, unsure about Android devices