Why does increasing the number of bounces make the back wall look so overexposed?
Isn't it because the amount of total light inside the room is increasing as the number of bounces increase? The green and red walls also get brighter and brighter as the number of bounces increase.
A slight caveat: the amount of light is not increasing, it's the same. It's simply that the calculated numbers are higher and higher as you continue with the recursion.
The fact that the reflection/ray tracing can get this good though after 6 bounces is so impressive!