Hey, so I think the main reason people don't use K4 is because of ELL. There are a lot of people that in general don't understand the concept of commutators, and the idea of using an LL method based entirely on a foreign concept scares them a bit (recognizing cycles and EO can be a bit tough if not experienced.) Also, I find the recognition of ELL to be awkward and a bit slow, but that can probably be chalked up to inexperience.
It should also be noted that the beginning of K4 is pretty awkward, and some people may not be comfortable with a method that doesn't have (as) efficient F2L. But this would be really easy to improve on. You could build Roux blocks, do L4C, use commutators to insert the last 2 F2L edges, and do ELL (but this is really just a less efficient variant of Lewis.) You can also take a basic cross approach (Yau and use K4 to build F2L and solve LL), or you could even make a ZZ direct solving method (although it would probably have a horrendous movecount); say, build LR centers, use OBLBL to make EO line, use K4 pairing to blockbuild F2L, and finally ELL. All have potential but I'd focus on the ZZ and CFOP based approaches b/c they'd be the most efficient and easiest to execute.
So yes it has potential, it's just scary to a lot of people; and while I'm no statistician, I would predict that it has a higher movecount than the main 4x4 methods. But if you could find a nice recog system I think it could be worth looking into, or maybe change the steps of ELL up a little. Maybe orient all the dedges and solve one so you only have 6 wings to solve?
