Hellob said: "^^^^
I think most musicals are going to be flat on tv. Even if they did another song there would be complaints. My shot doesn't let people know who is Alexander Hamilton and why is he hanging out with these guys. Furthermore, Lafayette and Mulligan's raps are so dense and fast that the audience could be lost and/or turned off. Possibly "Right Hand Man" would be a good choice but only if Colbert gave a set up explanation. I think the opening was the best choice for reasons others stated.
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I agree, with the Tonys they can take more liberties, as most, if not all, of the audience probably knows the musical to some degree, so they can do songs like Room Where It Happens (the one I personally hope they do) that are more high energy and show-stopping numbers. For the Grammys, a lot of the audience was unfamiliar with the show, and doing the opening number was a nice way to introduce them to it.
Generally though, I think I've heard more positive things about the performance from non-theater people who didn't really know Hamilton at all then I have from actual theater people. Maybe because we know the show and we know it isn't the best number? But it did what it set out to do, it brought musical theater to a wider audience and capitalized on a huge theater phenomenon. So props to them. I'd like to see musicals continue to perform via satellite at the Grammys, but it's probably unlikely, as I don't predict another show blowing up like Hamilton has for a while (though I would like to see more fantastic shows blow up!)