With so many bitcoin faucets site shutting down monthly, I don't think it is really profitable to run a bitcoin faucet site considering the time and effort the site admin would have to dedicate to the site. If the amount of satoshis reward is too low per claim, attracting visitors to the site would be another huge problem for the admin.
Not too much of an effort - free hosting, wordpress, plugin - you have your faucet site running like in 10 minutes.
Although promotion - is different issue...