They have a postal system in Equestria. They exist.
Don't forget that by the time Starlight's friend left, it wasn't just about him anymore. They could've exchanged letters (maybe they did; the Starlight only says she never "saw" her friend again), but it wouldn't have changed the fact that she'd had to sit and watch as a legitimately unfair system took her only friend away. From that point onwards the damage was done, and cutie marks were the enemy.
Even if her friend had come home, she still might've ended up on the path to Equalitown.
The backstory just needs to be expanded on. That needed to be page 1, not the whole story. Maybe they'll do that in S6, but it should have been done in this episode.
Maybe. I wonder if Starlight trying to find her friend might be a key plot point in S6?