No. While it might make things more fair for everyone, especially for poor Niney, I don't see it being a very good idea for a few reasons:
1: What happens if two people bid the same amount, and it's the winning bid?
2: No interaction. What works on a more intellectual game show like Jeopardy! will just kill the energy on The Price is Right. Or basically, it'd make the show less interesting to watch.
So while I can understand your wanting to change it, it just isn't going to work well on a practical level.