Is it safe to just store the coins on the exchange?
No its not safe, exchanges may be hack, lock your account (if they find something shady) or just run away with you coins, binance maybe good for now but not always.
That way it will be easier when I go to sell them and I don't have to keep paying fees for transferring them in and out. I realize that it's not normally advised, but with two-factor authentication enabled, does that change anything?
No, it doesnt change a thing, when a hacker hacks an exchange it can move free all the coins that he wants without the regards of security features.