Re. Pi 3
Yeah, also noticed this "feature".
I found out that many folks with the 3 just find an old fan from a small set top box or netbook and use that, for my ancient 3G/Wifi sharing Airtel b0xen added thermal pad and heatsink + micro fan stopped it frying.
Interesting idea. Read the thermal state and then change the sync rate to throttle the fan using the normally unused video output or a spare I/O pin.
IIRC the Pi can only output video to HDMI or composite not both but sync is generally on when Pi is active.
LM1881 would work fine in this application as 3/4 pin fan just responds to a pulse width modulated signal.
As my current projects include running Pi's at "Ludicrous Speed" (tm) this is very handy as it also lets me monitor each unit for failure so it can be rebooted by the MCP.