DISQUS

I don't think making a mockup/proof-of-concept will add much value to a fixed-price bid, neither that much of the effort in making a bid may be redirected to something like that.

Velocity on some selected use cases only tell you ... the velocity on those use cases. The problem is finding how many function points (or whatevers) there actually are in the specification, and velocity won't help you with that.

Usually you are supposed to supply a complete proposal for the whole spec, not just implement some selected use cases. So you still have to write the complete proposal, the "paperwork" that is supposed to be replaced by the mockup. In a bid you might include som "sugar", like screenshots and a detailed narrative on selected parts of the solution, but that doesn't take more than a day or two. This could be replaced by a mockup, but you might still want to write a description to explain to the customer how great this mockup is.

I just don't see how a mockup/proof-of-concept of part of the solution can help answering the questions asked by the customer in a fixed-price bid.