IIUC, the concern of using site engagement is that it makes the behaviors of those functions somehow unpredictable or inconsistent (something like, say, vibrate or top-navigation might work on some sites, but not others), and the developers would be very confused.
There were some discussions about exposing an API for developers to detect the existence of user gesture, but I'm sure if someone is working on it or not.
Do (or should) we have a similar API for site engagement score that developers can use? If yes, it might alleviate the unpredictability concern.
For maintaining the bit, should we consider same origin navigation (instead of same-domain)? For example, a user searches something on
google.com, and then get redirected to some hosted content on
drive.google.com after click, would we carry the bit to
drive.google.com? On the other hand, I'm thinking if the login/payment frames might change their origins during the process, say, from
pay.pay.com to
succeed.pay.com.