If you only have a 6x6 camera with you and you see a brilliant rectangle area, then go ahead and crop; but if you have the luxury of having a backup 6x7 with you, then you should rather use it because you will lessen the technical impact of enlargement. I'm just suggesting caution in the process of cropping/not cropping. I'm also pointing to the fact that it is worthwhile to be attuned to the specific impact of your tools upon your work, and not try to overcome them all the time.
The world around us is not presented in 1:1 or 1.25:1 ratios. The photographer gets to choose the way final images are presented and does not have to accept the proportions of a viewfinder. The right shape is right shape. If that is square fine, if rectangular fine regardless of the viewfinder shape you started with. Not allowing oneself this flexiblity surely is a compromise on the aesthetic qualities of the image unless size is more important - personally it never is for me. I would rather have a well balanced 12x16 than a 16x16 thats less good, if the aesthetics were stronger in the rectangular format. I would consider the keeping 4 unwanted inches pointless.
You say, "[cropping a 6x6 to rectangular] If you want to make an 20x24 out of a 6x6, you will need to do a little bit more enlargement than if you did it from a 6x7, and that could make a difference on your finished product. It's actually not a compromise: you're trying to maximise the potential of your tools." You are compromising if you think the image looks right as a rectangle but wont crop it because you dont want to waste 'neg area' thus sticking to a square!
Are aesthetics not more important than sheer size? Either way it is a compromise, but I take photos to produce things I hope are aesthetically pleasing rather than just 'BIG'