Interestingly, browsers are actually hiding a trailing slash here and then revealing it when one starts to edit.
https://example.com is browser-ism that obfuscates the true URL you are using — the true URL has a slash on the end:
https://example.com/
I’d be against dropping the scheme from the address bar when editing but don’t mind it being hidden for those who don’t want to show full URLs at all times.
I am in the camp of wanting to see the full URL at all times. URLs for all of their complexity are well-defined and the protocol/scheme in use is of critical importance.