Suppose that I already discovered only one branch for each truck brand. What do I gain from discovering other branches/locations?
What do I gain from discovering other branches/locations?
Nothing important, just different state/country plates for the location of the dealer.
Let's say that you buy a Volvo VNL on San Francisco, because you are in CA is going to come with a California plate. This happens with all dealers and states in the game.
This also applies to Euro Truck Simulator 2.
Some of them actually offer cool hauling contracts, where you get to haul trucks with your truck (hmm). I know at least a few Kenworth and Peterbilt dealers that do this. The only way to get similar contracts is from visiting one of the actual truck factories (which might in turn require various DLC maps, there is one in Seattle iirc).
Other than that, you have to buy the first 2-3 or so trucks directly from the dealer by going there in person. So it might be convenient early on to know lots of dealers if you don't want to fast travel for whatever reason (it costs a tiny bit of money). Later you can order them remotely and have them delivered to any garage, then it doesn't matter.
Also every dealer allows you to repair and sleep, so it's handy to know where they are for that reason.
Though mostly finding all dealers, employment agencies, landmarks etc is just a completionist thing. You might get Steam achievements and such.