The exchange you're going to send to will have its own fees (trades/withdrawal fees are common)
Storing coins on an exchange is not a good idea, if that exchange closes or gets hacked, then your coins might be gone forever. So you'll want to remove them from the exchange (which will probably incur fees)
Altcoins can be volatile (even more than bitcoin), what happens if while waiting for them to transfer to the exchange the price in btc drops 30%?