It developed over time. Used to be in the 60s and 70s (I don't know how long before that) that 4 man rotations were standard. a 5th starter was really just a spot starter. Throwing regimes used to be geared towards starting on 3 days rest. I think the first team to move to 5 starters was the Dodgers, and that was a bit similar to the situation the Nats are in now. They had an extra quality starter they wanted to give regular work to. It also used to be that teams preferred smaller pitching staffs and longer benches.
With expansion, there are fewer quality arms per team, so there is a big incentive to concentrate innings in your best pitchers. The reason you here people saying "he's a #3 starter at best, more likely a back of the rotation type" is sort of a short hand for an estimation of the quallity of the pitcher. To make up for the shortage in quality starters, teams went to longer bullpens and staffs. Used to be, 4 man rotation, 1 spot starter / long man, and 5 or 6 relievers were common. Now 7 man bullpens are the standard. More relief specialists make up for the lack of quality starting arms.
Most teams do not have aces, and when you have 2 aces and a couple of guys who could be #1 to #3 starters on all but the best rotations, there is a huge incentive to concentrate the innings in Strasburg, Gio, JZ, and Jackson. These guys are used to throwing every 5th or 6th day, so you don't want to mess up their tuning. Adding a 6th starter reduces your top 4 pitchers innings from 180 - 210 to 150 or so. While Stras is innings capped, you don't want to pull that many innings away from Gio / JZ / Jax. While we are unusual in that we have an innings limited ace and 5th and 6th starters that are rotation worthy, davey probably does not want to go with a 6 man bullpen and sacrifice a multi-inning reliever. That means we'd need a 13 man staff, and that really does not work well in the NL because it limits your bench to 3 subs and your 2d catcher.