Fast travel is just quality of life feature that allows us to trade few seconds loading for few (dozens) minutes of joging around ...

In other words if regular walking dont make our characters hungry ... it makes no sense for fast travel to do that.
And even IF it would ... we would not eat during the march but after during some resting time. :-/

In the words of the senior NCO instructor at cadet battalion:
“If you ain’t cheating you ain’t trying. And if you got caught you didn’t try hard enough!”