Frontier already has a number of unused ship designs in their concept art, some of them dating back to the launch days. The likely holdup is how much work is needed to actually model and texture them in-engine, create their flight model, balance the internals, weight, etc. Stuff that Frontier would still have to do anyway with such a contest.
Not saying it's not a good idea, I think it would be quite fun to see what the community comes up with. But it's not going to lighten Frontier's workload in any way. In fact, organizing, running, and judging such a contest would probably take far more of Fdev's time than simply hiring a concept artist outright.
Still though, it would be a fun community engagement project. We had something similar several years ago with a paintjob design contest, although that's a much easier thing to judge and implement than a full blown new ship.