Do I need a wallet?

Dumb question here but I’m confused - all that comes with having, say Trust Wallet, is needing to pay a small transferring fee to get my coins there (& more fees to transfer back to binance when I’m ready to sell?).

Also heard something about withdrawal fees off ETH being crazy high off Trust Wallet - so I don’t get why I can’t keep it on binance and withdraw from there (I’m guessing there’s def an answer to this i just can’t figure it out haha)

I heard it’s generally recommended to transfer coins to a wallet if we’re holding long-term on binance, but why? I don’t see any advantages.