You really haven't given much of a reason why this is a bad idea. Cut on image quality just to contribute to the "fairness" of a competition that's not theirs isn't really an issue, because the rules would be the same for everyone - and because of that, the perception of the individual would be bound to what everyone expects to be possible running that framerate.
What we are forgeting is that we already have a more or less mandatory framerate limit - and that is 30fps, due to TVs and what people have come to expect is a decent norm. Most games these days are 30fps. And a lot of them would benefit from 60, even the example you named being Heavy Rain. It might be a slow paced game, but everytime you're walking around, you notice how lag infested the controls are. Would it benefit the game much having it at 60? Perhaps not as much as other games, but by the same argument, I can also say that going for 30fps and having better visuals isn't detrimental to the game that Heavy Rain is - at least, we're not talking about severly making it an ugly game, just reducing a bit of everything to make it run at double the framerate.
If there are no games that run at half the framerate to compare them to, you wouldn't know how much better things would look but would rather just appreciate what you have.
Imagine a bit - how much better looking games would be if developers targeted 15fps. Would we really want that?
By the same account - graphics are cleary better on PC, so why are we still playing on consoles? Because there's more to gaming than just looking at nice pictures. Because people prefer to actually sit in a living room or just simply have that "plug & play" experience that you can't get on the PC. Because of that, there is a compromise - we live with worse visuals (compared to PCs) because we prefer the different gaming environment. So why would it be bad, if we just limit our expectations to graphics a little more for the advantage of having a better framerate (that benefits controls, responsivnes, motion of the game)?
What I am suggesting only works if everyone does it. If you have developers that are allowed to go for "half the framerate" to sell their games on the premise of better screenshots/visuals, other developers feel required to do so too.