This is beneficial to both parties, it's not just to throw spikes on the road for applicants without care.

The less nonsensical applications they get, the more time they can give your application.

> I understand that recruiters/hiring managers/whatever get a lot of junk applications, but frankly, it is your job to sort through them. You are paid to do this.

Indeed they are, and that is what they're doing by asking for a written application.