David Hayter was cast as Big Boss because at the time, he was the English counterpart of Akio Otsuka who is the japanese voice of Snake, Big Boss, and Solidus. I think Liquid has a different voice because he's supposed to be a different nationality from the other three? Or something... but the real "mistake" as it were would be Hayter not voicing Solidus.
Not to say I don't agree that Solidus having his own voice is cooler, Hayter would sound silly talking to himself but just saying... it's the japanese version that set the precedent that the "Snake voice" is something all the clones except Liquid share and Hayter being Snake in MGS3 was just trying to be faithful to that. If Cygan or someone else who had never voiced Solid was Big Boss, that would have been less faithful to what they were trying to accomplish in the japanese version which was mirroring Naked Snake and Solid Snake as part of the theme of the game.