BJJ is the best fighting style that fits the rules of MMA. Change the rules a bit and a different style will work better.
* Increase the minimum size of the wrist padding and gloves. Which makes it much safer to throw punches. Additionally, the design of the gloves can be regulated so grabbing someone is harder than it is now.
* Perhaps, add rules about how long you can stay on top of someone on the ground without doing significant damage. A lot of matches end up with a takedown at the start of a round followed by 3 minutes of light pounding and no serious attempt/success at a submission hold. A 20-30 second limit on no serious on the ground action will go a long way.
* Finally, we can directly change the judging criteria to make it easier to win rounds via striking dominance instead of grappling.
I suspect the most obvious answer is the same as the issue with other forms of grappling and wrestling - they are very good in structured 1v1 combat where there is a guarantee that a friend of your foe won't come along while you are both on the ground and bash you over the head with a large rock.