Did that and a lot of other checks and tests. Was on the phone for over 2 hours with 2 different advisors. First advisor took me to the point where I had to reinstall MacOS and, if that did not help, call back. Did not help so talked to 2nd advisor and we tried a few more things, then she talked to a senior advisor who indicated that this was a known problem to Apple and they were working on a fix, to either be pushed out "in the background" or in an update. No time frame for when this would occur.
Not being content to wait I continued fiddling with the Mail menu commands. After several other stabs in the dark I clicked on Mail->Add Account. Lo and behold, the pop-up window for selecting a provider showed up - but the actual Mail window opened up underneath it. So far it has stayed with me and is working fine - have closed/opened/closed/opened plus restarted computer several times. Also missing in the window was All Mailboxes under the Favorites section of the sidebar. Clicked on the little plus sign by Favorites and added the All Mailboxes back in. So...things looking good for now.