What's the advantage over having the user solve a captcha on the site itself?
Well, it's said that sometimes captcha can be failed to prevent the bot (RUMOURS).
So I think make it 2 captcha while gain more profit from the ads.
You can put 2 captchas on the main site. How does a url shortener stop bots?
Well cause some shortener url have their own way to stop bots, like AdFly, and I can earn more from them.
I think is shortened url bad idea. Faucet user like it when it is easier to claim earnings. additional clicks, captcha, "anti-bot" clicks did not work well.
also as far as I know some advertisements network do not allow to use shortened url
Yes no network except than phishy or NFSW advertisement network accept short url.
I personally think that most of url shortner service provide offer some sort of money to user to short valuable url. But most of faucet owner put their affiliate there for short url.. Most of link shrinking services offer interstitial advertisements which are shown before loading website.