I would be interested in learning about whether this could ever be possible. I recall the attempted 0.5*vsync change to the engine to allow us to set 30 fps - which, for anyone trying to create a game for mobile, was very attractive: 0.5 * the CPU and GPU work per second.... And that was a failure, unfortunately.
When I first thought about this having read the OP i thought that there could be a problem that stops this being viable - Tweak Guides on tearing. However, I'm not so sure now - that article is discussing GPU vsync rather than browser sync with GPU sync (vsync) of the monitor, so tearing may not may not be a problem. I don't know if it is possible to make a browser run effectively at half vsync using c2 because the 30 fps attempt went so badly.
But I agree - at 120 Hz refresh rate, the single thread of the browser that's running your game is working to do the same calculations in half of the time when at 60 Hz. And that means that some monitors could, in theory, cause frame drops just because they have such a high refresh rate.
Often GPUs allow the user to set the refresh rate - perhaps the solution is to state that, in the game hardware requirements, the user should ideally set 60 Hz.