Oh surely, yeah, relating to native languages is at best a crutch when it comes to getting to a pure understanding. But in this case I feel, it is a mere possibility, that whatever prime fundamental difference is added in order to get from the meaning of "go" to that of "ride", may share a very similar difference between "ходить" и "ехать", on a semantic level. Mainly what you said in the beginning
"it's more about moving without using your legs"
The English pair definitively exhibit a strong difference in use and emphasis, but this точный point could be the key trigger for the second word over the first in both languages, though in English it only opens the possibility of choosing "ride" over "go".

Also, again, knowingly perhaps overstretching the bounds of language comparisons:
"Trains go"
but in other contexts:
"Trains ride the rails"

Idunno,
I at very least feel I have gained a better understanding of the two Russian words from all this, seeing as the original material no longer perplexes me.