Generally, solid fuel is preferred in order to retain fission products in a readily removable form, which helps keep fission products from migrating to the environment. Liquid nuclear fueled plants would be impractical for commercial operation. The processing plant (to remove the fission products) represents a significant capital cost and potential liability.
Separating Xe (and Kr), and the elements such as Te, I, Cs, Ba and Se, Br, Rb, Sr, then requires some storage system to allow them to decay.
There is also the matter of core homogeneity.
It's not clear that higher burnup can be necessarily achieved.
I don't believe that the NRC stifles innovation. The NRC sets standards for safey and protection. Those are necessary contraints! Within those constaints, there is plenty of room for innovation. Developers of nuclear technology are more constrained by the cost of designing and proving technology, which is why the government(s) has played the major role in financially supporting the development of nuclear technology.