An MVP will tell you if it's even worth doing that UI design in the first place. If you can get people on your site going "I'd pay for this if only it didn't suck to use" then you have an MVP that's validated you have a market.
If you have a great to use product and can't get people to stick around on the site, you've wasted a lot of effort.
A UI is the M in the MVP. The back end would be a fair bit of work for nothing very exotic. I can test certain assumptions about the front end using public data without all that effort. Technically, it's probably a demo, not a true MVP, but it should tell me a lot about what works and what doesn't, and it shouldn't be too hard to expand into a true MVP afterward.
If you have a great to use product and can't get people to stick around on the site, you've wasted a lot of effort.