I've gotta agree with
@Movie2099 on this.
Most projectors are already capable of 120hz refresh rates. That's how they are delivering 3D and other functionality to end users and how eShift technologies have worked. So, if you start with a native 4K chip that can eShift and produce a couple of frames for every single frame, then it is already handling 120hz just fine.
So, the only thing that really has to happen is they need to add the front line inputs to accept 120hz. Processing has gotten insanely cheap. LG is doing it on their OLED TVs and Sony does it on their 900 series. So, if the processing is cheap, then it's just about implementation. It's basically a near zero cost upgrade/feature for end users.
They already make 'gaming' projectors. Optoma has a entire series they label the 'Game Time' (GT) series of projectors. But, they are all pretty entry level.
The real goal of any manufacturer should be to add as many zero cost features as possible to broaden your target audience without impacting your production costs. This is why 3D is still a feature of JVC projectors. It's a near zero cost addition to maintain. Having pixel shifting to enhance resolution is also inexpensive to do.
So, I fully expect that any engineer/marketing team worth their paycheck will be looking into this.
What isn't a zero cost upgrade is moving from a lamp to a laser as the light engine. This is perhaps the biggest question mark. How long can they realistically get away with making lamp-based projectors as others move towards lasers? I think JVC doesn't do themselves any favors when they release a VERY good looking laser projector for under $4,000 that's got plenty of brightness, then continue to use lamps in their LCoS models that cost a fair bit more. Eventually, they've got to go to lasers across the board. I'm not sure what will be the actual catalyst which will force JVC, Sony, and Epson to replace their lineup with laser-based light engines.