So a physical button is possible.
What you are saying is that it is dead easy just to throw a clear ap and sta mode or clear all settings because they are a little too persistent they persist after reflashing even with no username and password set it will connect to your wifi somehow. Yes they are persistent
You could though just enter no settings at all leave it as is and add to your program a branch that would ask for your wifi and ap info. It may short you a few lines of code for each but still there would be about 200 lines of code available to make stuff happen.
this way you would just connect to esp type in http://192.168.4.1/msg?wifi You could make it so that this URL technically would be the way you access these settings and you could even add a clear button on this page or you could simply create a webpage to do these settings and store it on the device as well and access it this way
http://192.168.4.1/file?file=wifi.html
There are a ton of ways to do it while keeping the persistent settings for folks that need them I believe mmiscool (WHILE I AM NOT SURE OR TRYING TO SPEAK FOR HIM) is trying to satisfy both ends of the spectrum and this was a way for him to do it.
Where I buy my ESP8266 boards from... (Banggood)