Two Factor Authentication Train Wreck

I had a back experience with 2FA, and I can't figure what caused the problem. Has anyone else had a similar problem?

Here's the saga of my nightmare with "two factor authentication."

I followed the guidance of Apple that 2FA was a good thing to do. I followed the instructions, and voila my iPhone, iPad and MacBook Pro were all authenticated with the new system, all three could receive codes and were trusted devices.

Then I needed to created an app specific code, so I went to (as per instructions) my Apple ID page. In my Safari browser on my MacBookPro, I put in my Apple ID log in information, and then a verification code number appeared (as it should have) on my phone. I entered that verification code, and I was logged into my Apple ID page... but only for about 3-4 seconds, and them was logged out. I tried again, and again, and again. Same replicated actions and events, time after time.

So, I try then to login to my Apple ID from my iPhone, and iPad. Each time, after I entered supplied verification code, and I am logged into my Apple ID page... but only for about 3-4 seconds, and them was logged out. Just like with my Mac; and so I tried again, and again, and again. Same replicated actions and events.

There seemed to me, obviously is a two-factor authentication problem, as I never had this problem previously. So, I go to turn 2FA off. However, I can't find a way to do so on any of my devices (no "turn off" option is available). What to do? Well, I check out details about how I can turn 2FA off, and I find some instruction from Apple which tell me that I have to... wait for it...

"Open any web browser on any computer and go to appleid.apple.com [then] Log in to the Apple ID... you want to disable two factor authentication"

The Catch-22 was at hand. So, I call Apple tech support, but it's too late -- they are done for the evening. And so I am stuck. Finally after playing around enough, I try changing my password from a link in the initial Apple 2FA verification email (even though my iCloud password works just fine), and when I do that there a blue button at the bottom of the change password screen that allows me to turn off 2FA if I change my password. I do so. And 2FA is no more. Quietly, I promise myself that I will never use the nonsense that is 2FA again; having wasted of 90 minutes of my life for no good reason.

So, now without 2FA turned off, all works fine again; I updated my iCloud password on all my devices and all of them work fine again.

I have had an Apple Computer of one flavor or another since 1984, and what I always loved about them was they just worked, and worked easily. This is perhaps the first time that I had the experience of an Apple device making my life more complicated. I hope it never happens again.

Any idea what happened? Has anyone else experienced this?