Based on the description on their site, the controller includes a built-in battery: "8.39 Wh Li-ion battery, 35+ hours of gameplay... "
That was disappointing for me. Specially condidering the Steam Frame's controllers make use of AA batteries: "One replaceable AA battery per controller, 40hr battery life"
AA Batteries might not be as convenient to use, but being able to replace them is a great advantage. All my Xbox360 controllers still work fine, but none of my PS3' Dualshock 3s.
The official docking station could be used to recharge (rechargables) AA batteries so the functionality could remain the same.
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 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.