2 minutes every few years?
What? Where are those numbers coming from? You’re going to plug the controller in for <1 minute/year!?
Why do you need to replace the battery after only a few minutes of use? Did you miss that you recharge it in the controller?
You only need to replace it when it no longer holds enough charge to be useful, which is going to be at least a couple of years. You're not replacing the battery in your phone every couple of days, are you? Why would this battery be different?
Your edit:
I’m not answering the same questions yet again.
I did not ask any questions in my last comment that I had asked before. You have never said why you think you need to replace the battery in the controller often enough for a screwed-down battery cover to be a problem. You have never said why the battery not being AA-sized makes it take longer to replace, when there are many quickly-swappable battery designs out there.
You have tried to say that the Steam Controller won't be like that - but without evidence and without acknowledging that you said something wrong. That's not very good.