In the first public reading of the show, Burr was played by Utkarsh Ambudkar, who is, like Miranda, a stronger rapper than singer. I don't know how much of the show was yet to be written at that time (they only performed Act I and a few excerpts from Act II), but it is indeed very possible at that time Miranda was still considering playing Burr himself. He made the right choice: the way Burr and Hamilton exist on the opposite ends of the hip-hop spectrum (Rap vs. R&B, I mean) underlines the central conflict between the two men rather beautifully and it would have been undermined if Burr was a more rap-heavy role.
Frankly I find the debate over whether or not Lin has a good enough singing voice to do justice to this role kind of pointless. Hamilton doesn't do a tremendous amount of singing - about 2/3rd of his part is rapped rather than sung. What is sung is not particularly high or sustained. His actual melodic content is pretty limited. The first thing he has in the show that could really be called a siginificant amount of singing (as opposed to rapping) is "Dear Theodosia." And honestly, while Lin does not have a classically beautiful instrument, he uses what he's got extremely well. He acts with his voice. He has a fire as a performer that, frankly, is an ideal match for his character. Munoz is smoother, cockier. But Miranda is a livewire.
I haven't seen Jon Rua but a report from a friend who did at the end of the month was that he reads (and sounds) a lot younger than either Javier or Lin. This worked really well in Act One, apparently, where Hamilton is a kid trying to prove himself, but it made his scenes with Philip a little harder to believe.