Ignite scales with levels and does true damage, so it doesn't fall off that hard late game. It's 50% reduced healing is also pretty handy against at least 1 guy late game. Fighters and tanks in general have solid sustain, marksman have life steal, supports can occasionally heal allies, and summoner heal is a thing.
Also, true damage.
Ignite adds an extra ability to your burst rotation, which is pretty useful if you were trying to ~60%-->0% your opponent in the first place.
Going off of a fairly low ~2.2 AP ratio for an entire QWER combo on a standard mage - Ingite offers the rough equivalent of 32-186 AP from levels 1 to 18. You don't get interactions with things like Lich Bane and Rabadon's, but it is True Damage - which becomes more relevant the latter a game drags on, as magic resistance gets progressively higher.
That said - mid lane doesn't always go for Ignite, it's just handy to have more burst when you were going to burst in the first place.
A lot of pro players are going with Teleport instead.