Here's my theory:
No one is born with boots. They put them on. Koopa Troopas are like humans, as in they can walk on two legs and crawl on all fours. They used to crawl because the levels in SMB had areas with low ceilings in which they had to crawl underneath, like in 1-2. As shown in SSBM, When you stomp on a koopa, his wings fall off and he falls. It's like Mario shrinking when he hits an enemy. A koopa loses his wings, and then his shell, or sometimes just his shell, if he isn't a paratroopa. Yoshi isn't born with boots, but he is born with the saddle-like thing on his back, as it isn't tied onto him and would fall off if it was just a saddle. Yoshis have the red spikes, so apparently, the "saddle" looks like a flatter, wider spike. And no one is born with boots.
I wish I was in the forest with a dragon right now.