As a complete WAG, I would say that as you rev the engine the greater RPMs up the output from the dying alternator. So, maybe the fan isn't actually speeding up when you bring up the RPMs so much as it finally get the juice necessary to run at the right speed.
I guess it could also be overcharging. Seems like the battery would let you know in that case. Wouldn't it be getting really warm if it was getting too much charge?
Just guessing
