The wallet is for when you have a lot of coins, or you're going to hold onto something long term. You take it off the coinbase server so that in the event there's a hack, or the servers are down you still have yours. A lot of coins have their own proprietary wallet you can put on your PC / Phone, and then there's hardware wallets that take your coins completely off a computer or phone with no connection to the net at all.
So basically, in regards to the big 3:
1. You use coinbase to purchase them with US dollars,
2. You transfer the amount of the big 3 you want to keep untouched in your wallet.
3. You transfer the amount you want to trade-in for alt coins in Binance
4. You put any alt coins you want to keep untouched in your wallet?
Wash, rinse, repeat?
Then say it's time to cash out on an alt coin (or any of the big 3)... at that point do you sell them back on binance to get BTC and then transfer that BTC back to coinbase to cash out?