I have heard this discussion before (though not on here), and I think that's a pretty good idea, if we could fit it in the story. Personally, I don't really see it fit with the PT as it is.

It fit in the story of the OT because it was Han's personal ship and we spend a great deal of time with him. But this doesn't really apply for the PT. I think this has to do with the bigger scope of the PT: we see more characters, more planets, more cultures and the trilogy plays over a longer period of time.

For example: the Naboo have their own distinctive style of ships, but we only really see those in TPM because the story is set there. In AOTC, Amidala has her own ship, but it gets blown up. The Jedi also have their own fighters in AOTC, but those have changed again in ROTS because the visual style of the movie is trying to move towards that of the OT.

Also, having a hero ship in the PT just because the OT has one sounds a bit like repeating itself, like Lucas is already accused of in the PT.