This has nothing to do with branching storylines.
My question is as literal as possible. If you're on a world map, and there is a dirt path/road to where you're going, do you follow it? Or do you just go the shortest straighest route?
Depends on the game.
For Zelda 2, sure I stick to the path where available. Each encounter takes time and resources are limited once you set out from a town.
For Dragon Quest 5, there's not much of a difference between sticking to a path or not sticking to one, so I typically aim for straight from point A to point B.
For Advanced Wars, Trucks like Scouts and Missiles are going to need roads as much as possible since their mobility tanks elsewhere, though Mechs are slow as shit no matter what you do, so its best to let them march wherever like a flood.
For FFT, it's menus all the way down.
And for Beyond the Beyond, everywhere has a ridiculous encounter rate, road or no, and its just simply better to not bother at all.