So the contract does two things.
Firstly, it gives you a legal basis to enforce breaches.
You set out what you are going to deliver and the payment terms and then you both agree to it. You deliver as promised and the client doesn't pay. That's a breach of contract, everything's laid out unambiguously on the piece of paper and it's got both of your signatures to prove you both knew what you were letting yourselves in for.
So, at enforcement time, there's much less room for argument.
But, secondly, and more importantly, the contract sets expectations.
By having a formal contract, with terms and conditions within it, you are saying to the client "I'm not some no-mark who's just chancing it". You're saying "I am a professional, and I have a set way of doing things that is borne of my expertise". You are saying "this isn't some trivial arrangement, it's not some game, this is a formal relationship with benefits for both parties, so please treat it seriously".
And by making those expectations very clear from the off, you're going to scare off the chancers and much less likely to get burnt and have to go down the enforcement route.