The mishna deals with amputees, and the leather 'semuchot' that they would wear at the end of the stump, in terms of going into the reshut harabim with them.

Interesting question: In the beginning of the mishna, where he literally walks on his thighs, and these semuchot protect him, the mishna allows him to enter into the beit hamikdash, because these aren't like regular shoes.

Yet at the end of the mishna, when he's in a chair (Rashi describes it as an actual chair; no wheels), the mishna says he can't go into the beit hamikdash, as they are considered shoes. What's the difference? In either case, he has a stump, he's not walking on the stump, and it is being used as protection? Why are the two cases considered different?

Maybe we're machmir for kedushas beis hamikdash. It would be unreasonable to expect someone who is using them to protect his sensitive skin while putting pressure on it to disallow him from wearing it, but maybe that's not the case if he's sitting.

Possible answer: In terms of using a cane on shabbat, one may only do so if they absolutely need it to get around. If they can be mobile without it, they can't use a cane on shabbat.

So to here, since the person can get around in his chair, and doesn't abolutely need it to get around, we don't let him go into the beit hamikdash. Whereas the person who doesn't have a chair needs the semuchot to get around, we let him go into the beit hamikdash.

Actually, isn't the original pshat of the mishnah that the "semuchot" are on the chair?