I'm not as fit as I thought I was

[exxxviii]

Yes if you walk at least 6mph (10 minute mile) or higher it would start becoming less effect than running at that speed, so technically you are correct. However I doubt there is anyone reading this that can walk an under 10 minute (complete) mile so it doesn't really apply. However here is a chart to qualify it.

My point was more in comparing a typical 4mph brisk/fast walk to a moderate 6 or 7mph run.

Ditto, I just a slightly different inflection point between the two. Data I have seen puts the crossover at around a 13-1/2 minute mile, where you could either fast walk or slow jog. I was just trying to add that running is not inherently inefficient, it is just different than walking and far more efficient at faster speeds.

Those Olympic speed walkers are probably significantly less efficient than a runner at the same pace, which makes the speed walking all that more impressive.