@PENG - I have a 7.2.4 configuration with 7' VMPS SuperTower III setup as surrounds. When I use multi-channel stereo it's to pair the bold sound of these monster towers with the high definition of the Ascend Sierra Towers with RAAL 70-20 tweeters (along with height speakers).
The Denon volume control has to be down by 10 clicks to level match with stereo mode vs multi-channel. You can play much louder or drop the volume as you suggest. I can't speak for others but when I play in multi-channel mode the preferred volume is almost always louder. In addition, the Monolith7 offers over 300 watts per channel with 4 ohm speakers like the Sierra Towers.
Maybe my Denon 4500 height channels failed prematurely because the hardware was marginal? Or maybe multi-channel does cause additional strain? Or maybe when I used height channels as "B" fronts that caused a strain? I would need about 20 receivers to test each option with and without external amps.
I understand your theory is the same power used over more channels should not add strain - but, I think it's more normal that multichannel is used with significantly higher volume levels rather than the same level.