My problem is that I have two iMacs running Mavericks (for specific reasons too long to go into here). Everything was fine until a few weeks ago. They are at two locations. First sign was issues with iCloud on the computer. Can't remember now exactly what the issue was, but I was basically forced to delete everything, then resign in. That's what the language of the popups indicated. So I did. What a mess! But I was able to do that and get signed in, and then re-sync to the Cloud.
Then I checked "Find My" (no longer "Find my iPhone" on iOS13) and it renamed that computer to ERASED MAC and could no longer pinpoint location, just shows "online". That was scary. The iMac was was NOT erased (but I had to erase the contents of iCloud on that computer). The name was not changed on my iPad running iOS12+. I was able to sign back in to iCloud and select what to sync and it seems to be working? CS had no idea what happened. It seemed to be a "Find My" iOS13 issue.
So I finally get home, and turn on the twin to that computer. First thing I notice are some oddities with Mail and iCloud account (seems to have dissappeared?). So I go to System Preferences to check iCloud. I am signed in, but can not access ANYTHING unless I enter my iCloud password. So I do. THEN, it says it needs the code from my device. But there is no place on the iMac to enter it! Once I enter my password, the window is gone. For good. Unless I close System Preferences to trigger it all again. So I tried to trick it and do it all quickly, so I could add the 6 digit code to the end of my password (while there was still a box to enter it). Didn't work.
So I sought a way to TURN OFF 2FA even just for 30 minutes so I could get out of this loop - and NO... you can not do that!!!
My biggest issue is that it was NEVER MADE CLEAR ANYWHERE that I would never be able to turn it off (after the 14days). My second issue is that I received non-stop nags to turn it on before I was ready to during a switch around with 2 AppleTVS, 2 iPhones, iPad, 2 24" iMacs and a 27" iMac. I might have turned it on - just to shut it up, but wasn't done with my setups (which made it a HUGE pain in the arse). But to be honest, I am not sure if I even did that. I think what really triggered this whole slippery slope into chaos was getting a new iPhone 11 running iOS 13 (or maybe just updating the previous iPhone to iOS13 a couple of weeks earlier?)
In any case, I did not have any problems with iCloud (except the occassional inconvenience of having to run to another room to find a trusted device) pre iOS 13. I guess they decided that Mavericks needed a downgrade at the same time? Because even though it is admittedly old, iCloud worked fine on it - until iOS 13 was released. Yet oddly, if you log in via a browser... it still uses "Find my iPhone" (not just "Find My").
And yes, I have complained through the regular channels... but seriously doubt they care or read anything there anymore.