I think the "real" problem is not matching shutter speed to frame rate. With 24fps you have to make a strong choice - either the shutter speed is 1/24s or 1/48s, or any panning movement is going to look like absolute garbage. But, with 60+fps, even if your shutter speed is incredible fast, motion will still look decent, because there's enough frames being shown that the motion isn't jerky - it looks unnatural, just harder to put your finger on why (whereas 24fps at 1/1000s looks unnatural for obvious reasons - the entire picture jerks when you're panning).

The solution is 60fps at 1/60s. Panning looks pretty natural again, as does most other motion, and you get clarity for fast-moving objects. You can play around with different framerates, but imo anything more than 1/120s (180 degree shutter in film speak) will start severely degrading the watch experience.

I've been doing a good bit of filming of cars at autocross and road course circuits the past two years, and I've received a number of compliments on the smoothness and clarity of the footage - "how does that video out of your dslr [note: it's a Lumix G9 mirrorless] look so good" is a common one. The answer is 60fps, 1/60s shutter, and lots of in-body and in-lens stabilization so my by-hand tracking shots aren't wildly swinging around. At 24/25/30fps everything either degrades into a blurry mess, or is too choppy to be enjoyable, but at 60fps and 1/500s or 1/1000s, it looks like a (crappy) video game.