Funny you mention it, I recently purchased a current meter to measure electricity usage on my computer at idle/load, and I tested my receiver with it. The receiver puts out 120w per channel into 6ohm, or 75w into 8ohm, 5 channels. Speakers are 6 ohm @ 87db sensitivity, so they are relatively hard to power. Total electricity usage playing 5.1 material at 0db gain (really loud): 40 watts and 3.5 amps for the entire receiver. I can't specify how much was going to each channel, but it must be a fraction of that, minus the power required to run the DSP chips, LCD screen, etc. The amount of power amps really put out is overblown. You'll never see the staggering wattage figures on the box in real life. Ever.
Your power measurement test was fine, but won't reflect the actual power delivered to your speakers on an instantaneous basis. Here's why: Using 5.1 material, none of the channel's signals are identical, and that means that it is unlikely that at any moment in time all channels will be producing full power simultaneously. For that to happen your test signal would have to be a continuous sine wave of equal amplitude produced simultaneously in all channels, a condition not found in program material. Next, program material is constantly changing and has a rather high peak to average ratio, on the order of 8 to 10dB. So if you did have peaks at 75 watts, your average would be 7.5 watts. Now, that doesn't mean you're not actually using that 75 watts, it just means it's very momentary. Then there's the power supply in your AVR with it's biggie sized filter capacitor storing energy up then dumping it out during high power peaks, then re-charging more slowly over time. This has the effect of smoothing out peak demands that would be reflected back to the AC line, and producing a long-term average power that may seem unusually low.
Here's your test: Produce equal level, frequency and phase sine waves in all channels, run your gain up to whatever setting you like, and now measure your power...quickly before you blow all your speakers. You'll now measure the total power delivered from all channels to the speakers plus the quiescent power load of the AVR times the efficiency factor of the AVR (not published, but probably not much over 50-75%. The difference between the total power used for speakers and AVR and what measure is a result of efficiency, and that power is just heating up your room. The other variable in your test are an arbitrary 0dB gain (unless you've calibrated the system), and whatever "really loud" is. Levels are important in power testing as a +3dB change is a doubling in power, so you can't really fudge the levels and get a meaningful power measurement anywhere in the system. And lastly, the impedance curve of your speakers. Single figure impedance specs are misleading, they might dip lower or peak higher, and you'd want to know so when you pick your test sine wave frequency you land on a known speaker impedance as well.
Now, do you NEED that 75 watts? Probably do, at least every now and then, if you're playing 5.1 soundtracks near reference. Considering your front three only at 87dB sensitivity, you'll max at 100dB SPL at 10 ft, which is slightly below what you'd need for real reference level undistorted playback of all soundtracks. That's because the reference is 85dB SPL, and there's typically 20dB of headroom between average program level and highest recorded peaks. So, if you play at reference (most people don't), you'll clip early with your setup, probably by 5 - 7dB.
But, in a discussion of speaker wire size, this is all sort of besides the fact. The circuit of speaker and wires forms a voltage divider which works at all volume levels to modify frequency response, depending on the impedance curve of the speaker. So, less series resistance means less wire-induced response modification. In the recent post here, I mentioned that a short length of small wire won't matter, and that's true because its total resistance is very small.
Wire-induced response modification is mostly viewed as undesirable, but there may be specific cases when it is of some benefit to the overall performance of the system. It is not an optimal way to achieve a response modification, and is not generally recognized as desirable.
Wire heating is mostly based on long term RMS voltage drop, so the low average power you've found is more appropriate for that discussion.