1. It's too easily countered. Being able to face-tank a heavy for a few seconds is nice, but this is TEAM Fortress, usually there is a soldier/demoman/pyro close by that will murder you while you're ubering with bullet resitance.
2. It's really clunky. Having to cycle between 3 resistance types is unnatural and just a general pain in the butt. It also adds to the confusion of hitting the cycle key too many times, and getting thrown off of what resitance type you're on, which often leads to death.
With that said, I came up with some changes that could kill both birds with one stone.
Change 1. Add melee resistance. It makes sense and goes well with the Vaccinator, and people have been asking for it for over a year now.
Change 2. Combine fire resistance with explosive resistance. Combine bullet resistance with melee resistance.
This way, the problem of cycling between 3 resistance types is completely removed. However, the Vaccinator remains balanced because the user has to choose between fire/explosive and bullet/melee. The only difference now is that the Vaccinator is more difficult to counter, which is exactly what it needs.
There is a reason almost no one takes the Vaccinator seriously, but I think these changes could really make it something worth using.