Beating 2-Factor Authentication

I can imagine how it goes.

The provider implements 2FA to its clients, using text messages only.

Clients adopt it. Then, clients claim they are not getting the text messages.

Business asks for IT: “Please, improve the 2FA system, texts messages are not enough”
IT thinks: “Ok, we can call the client if text messages are not working. Should we submit this system change to CSO approval?”
Business answers “No, it will delay the process and it is only a minor change”.

The rest of story is below.