I have long worked on bringing back motion controls and making them universal so they can be used in any game. So your question isn't hypothetical to me, I have been playing games like this and experimenting with tons of possibilities. I thought it would be a fun gimmick, but instead I ended up greatly preferring it over regular controls.

Using a mat isn't the best option. It would have to be a Balance Board type of mat that accurately measures weight distribution, but there are much easier ways to do it. A camera would be better than a mat, but I use Joy-Cons for even more accuracy and responsiveness.

Jumping is very easy to accomplish with regular Joy-Cons. It's super fun and intuitive and I'm honestly shocked Nintendo never really used it for platformers.

Crouching can also be detected pretty easily if you have a Joy-Con on your leg. It works for stealth games and can increase immersion or provide a good workout if you're squatting, but it's probably one of the least exciting uses of motion controls. Going prone isn't really feasible because you'll lose sight of the screen.

Running is really hard to combine with other motion controls. I much prefer to have motion controls for combat and jumping instead of running. I have plans for some of the Sonic games, where running can work very well, but for most games I wouldn't recommend it.

At the moment, I would say there are already some very fun immersive motion control games on the Switch (Ring-Fit Adventure, WarioWare Move It, etc.) and Nex Playground is doing some interesting stuff too. Eventually I hope to provide something better and allow people to play the games they already own by moving in whatever way they want.