Well since the public release of iOS 10 is now available, I decided to put this to the test myself and report back for the benefit of all of us.
Sadly I can report the problem persists.
Steps taken: 1) switch mail slider to off 2) re-open and close mail app to make sure mail account was cleared out 3) hard reset 4) update to iOS 10 5) re-enable mail account 6) verify all phantom unread messages were gone (they were) 7) resume normal use
The very first time I cleared the junk mail folder went ok and the unread count remained zero while it showed No Mail. However, a little later once I had collected a decent number of junk messages (say more than a dozen), I went to delete them all. In iOS 10 I no longer see any option to Trash All. I had to click edit and manually select all messages and press delete. Upon doing this it left 2 unread messages in the mailbox even though it showed No Mail. At the time of writing I am back up to 6 after another couple of rounds of purging junk mail.
I find it deplorable that Apple would have such a terrible mail client. It has definitely stolen the thunder from the enjoyment of a shiny new mobile OS.
Perhaps it is just my device and the only way to permanently fix would be to set it up again as a new device. I suppose I will find out soon enough when I receive my iPhone 7 Plus in a few weeks.
I do regret not completely deleting my Exchange account before the upgrade to iOS 10 and adding the account back after. However, it is worth noting that upgrade aside, I have take that step several times to no avail besides a temporary relief of the phenomenon.
I will be hoping to hear something encouraging from one of you in the meantime.