There's two problems I can see.

First, the aerodynamic modeling of the entire rocket is based on the known shape and mechanical properties (sturdiness) of the fairing. A different fairing could lead to different loads on the rest of the rocket, make it respond differently to steering etc.

Second, the fairing has to be really really strong. It takes all of the aerodynamic loads on the rocket. They've been able to put a lot of effort into making it strong and still light because they always use the same fairing. If you are designing a custom fairing then you have to make sure the ability to transfer loads through the payload makes up for that advantage. That seems kind of difficult, especially since an inflatable does not need any load-transferring structure in the middle part.