You submit it to TASVideos.
And there's lots of reasons.
Challenge yourself. Discover new tech. Gain a greater understanding of the game. Create the perfect run. Compare tricks/routes and determine what's faster.

TAS runs are really fun to watch. Perfect play is very entertaining. Also, a lot of new tricks are discovered by the TAS community. Also, TAS runs have their own website.

ohhh okay thank you

This video explains why:

Leaderboards aren't everything. In the grand scheme of speedrunning (both TAS and RTA runs) this website and the leaderboards themselves are rather recent.

Apart from being a pretty large thing in speedrunning itself it is a good theory crafting tool to see just how fast a run could possibly get, as you can also use TAS to create the "perfect" run that can still be performed by a human. Or a good tool to use for routing to test strats. TAS does more than you think towards helping people even get those top times to begin with.