Why do they use it? The -30% all damage is an extreme disadvantage. There are so many ships other end game ships with way better stats than it. The only reason I think it could be useful is because of the healing spray. But even that could be transferred from one ship to another! So again, why do people still continue to use it?
First, the -30% damage is not an extreme disadvantage. Like all other ship specialties, it doesn't change the ship's base damage; instead, it's added to your % damage from artifacts. Even if you used % damage with medic, the +75% attack speed bonus will increase your DPS much more than the -30% damage decreases it.
However, most people don't use % damage builds on medic; they use flat damage and weapons that work best with flat damage (e.g. Gatling Gun) instead. With this setup, the -30% damage is even more of a non-issue; the base damage of your weapons is so small that getting 30% of it subtracted from their total damage is totally insignificant with good flat damage artifacts. The +75% attack speed, on the other hand, gives your DPS a large boost, even if you already have good attack speed from artifacts. This makes the Medic one of the best ships for flat damage-based setups in the game, even at endgame.