Stop the "don't lose access to your account" nonsense.

Correct, everyone has Azure (it is wrapped around the MSOL DB where all of our identity information is stored), that is the identity management portion of O365, we all have it.  And thanks for the info (@Tarran and @Niklas Fritz) about what to search for and all.  I checked for the group in Azure AD but didn't find any even close to that name (or portions of that name).  Also users enabled for password reset was already set to NO (since we only use on-prem AD and SSO for auth).

This happened to us a few months ago so I complained about it then and it was resolved at the time (within a couple of days of complaining).  I noted back then that there was an "Identity portal" outage in O365 at the time it was resolved.  I gather that the "outage" was to undo portal code so that this "feature" wouldn't keep popping up.  I also gathered that the code implementation change was impacting me because I am part of the Early Release thing that MS has.

My own two cents…for us (admins), the problem is that MS doesn't take this stuff very seriously.  And we Admins are the ones that need to support O365 on the front lines and we are the ones that recommend (or don't recommend) O365 to other people.  Common cents would think that if MS wants to increase their O365 presence then they would understand that aspect of it.  Just because they put Enterprise in the licensing name doesn’t mean that they are offering an Enterprise product.  Things like this give O365 (and MS) a bad name within the admin community.  And just like VISTA flopped because the admin community didn’t adopt VISTA, O365 can do that to in a turn of a dime.  MS should wake up and listen to what the O365 need.

Tarran, You may want to let the top level Microsoft techs know if can be turned off for Global Admins because after 2 hours of looking they said it can't. I already have it turned off for regular users.

I have a personal tenant but no Azure subscription. Regardless, a competent service would have this turned off by default and available as a simple straightforward option if required by customer.

every O365 tenant uses Azure

I have at least one tenant that doesn't use AD or Azure, and I still don't see anyplace to turn it off within O365.