I don't think that's a real problem.
120Hz single strobe is good enough for most. I think that people who can't stand 120Hz flicker, are a microscopic minority.
Stroging at 60Hz is a real problem, though. With 99% of console games not supporting any higher mode that is low persistence (strobing) friendly, and with even some PC game ports being capped at 60fps, it is a real problem.
Flicker doesn't have to be a problem though. This in my opinion just depends on the developer's choice. If they choose to not offer stable 120fps on consoles, or support for attainable 90fps (for the less allergic to flicker) to 120fps (good for most people) on PC, then that's their mistake. If this mistake creates the flicker issue as a result, as it forces people to torture themselves with 60Hz flicker, then it's still a dev's mistake problem, not flicker problem.
Also, people are lazy. For some people who say they cannot tolerate any flicker, using strobe modes on PC will be way more problematic if they spend most of the time outside of gaming. If you finish your game and start using a word editor with full screen white page, then yeah. Strobed mode will not have any benefit but the flicker will be tiresome even for people who don't see it.
Again. This is a problem of wrong approach. If there was any will and incentive to do so, there could be an automated mode coded into monitor's firmware or otherwise. If full screen of white page with text on it was detected, it could trigger the switch. And with that, I'm sure a lot of "I can't stand flicker" people would leave that already tiny group.