Alright, so I looked into this myself a while ago, and frankly the issue with going over 60 Hz is that the graphics cards simply can't push that many pixels that fast. Doubling from 60 Hz to 120 Hz doubles the pressure on the GPU, which is already intense at 5k. With thermal issues / power draw in consideration, the technology just isn't there for anything past 3440x1440 @ 120Hz. Even then, you're looking at a 1,200$ monitor to get there that is limited to a particular flavor for GPU (FreeSync for AMD, G-Sync for NVIDIA). Since Apple uses their own flavor of vertical-sync in their GPUs for their screens, it is unlikely that Apple will push past 60 Hz in their monitors, as opposed to increasing resolution to 8k or beyond while maintaining 60Hz refresh rate.
As a biological note, the refresh rate of 60Hz is much more noticeable in younger people than it is in older people. This has to do with how the human eye changes over time. Most of the tech guys in my family can attest to being satisfied by lower refresh rates as they got older, but early on we prefer 75 Hz or higher even on LCD panels. Being on the younger side myself (mid 20s), I can visibly see the difference between 60 and 75 Hz. Anything lower than 60 Hz does give me a headache as well, so I can relate to the OP's problem. (This is after having worn glasses most of my life).