It's a nice app from a UX point of view, but you are right - this is a glaring hole. Workaround for now is to tap every time you suspect something.

I believe there must be a couple of really good alternative mail clients on iOS. I am interested in what you find.

iOS Mail is sh*t in plenty of other ways, too.

Might anyone here have an alternative to suggest? Preferably a strictly-local one, with competent security - vs. ones with "they copy your whole mailbox into their Swiss-cheese cloud" stories all over the web.