The reason you get hydra is because it gives you ridiculous sustain in situations in which you'd be at a disadvantage prior -
Being inside a large wave of minions or diving for a particular enemy and having their team engage you (usually within that melee range, lol) equates to considerable amount of health gains.
Like, Auto -> Hydra -> Auto will be giving you 400+ health heals inside minion waves, and depending on enemy tankiness, less but still relevant.
This means with a hydra, chasing someone into a minion wave (especially if you ignore unit collision) is actually a really awesome scenario. You'll be having access to a ******** sustain mechanic engaging someone 1v1 who'll naturally be weaker against you because of tiamat/hydra's AA reset, 100% of base AD extra burst, dat sustain (most likely).
Although tiamat helps these scenarios by killing creeps who'd otherwise be applying tons of damage to you, only in the champion case is it extremely helpful (mitigating damage) to have hydra over tiamat.
For this reason of being able to jump someone in waves, I find any melee with a gap closer + tiamat (and hence beyond) beats almost every AP mid, and likely everyone else who doesn't buy the same item.