With those small amount of coin from faucet, you can play with send or receive to familiar your self with those functions of bitcoin. That is very valuable.
Possibly not right now. Faucets have relatively low payout rate and it takes a few days to even cover the transaction fees assuming you do take a break and sleep. Furthermore, most have a high withdrawal threshold which can increase the time. Some uses online wallet API to transfer coins offchain too.
Who would spend days doing faucets? Their time is not worth much or if you say no sleep or break to do them, then their life is not worth more then $1 an hour?
Sure time is money but put your time into something worth more then a fraction of a penny per click.