When we make a proposal we include a project scope, pricing and payment terms. Before we start work we exchange contracts, collect any down payments and sign off on the project scope. The two, proposal and contract, are connected so that we have a firm legal foundation that we know will cover all the likely contingencies.
But the basic reason is that you the client will know and agree to what we are going to build and how much bang you will be getting for your buck. We then also know the extent (scope) of the project. We find this minimizes any misunderstandings.
During execution, working with the client additional great ideas often come up and these can be folded into the project in a couple of ways. Either we can add an additional Statement of Work or prepare a separate phase 2. Clauses in our contract cover such circumstances.
In this way, an exchange of documents keeps everything professional while providing a lot of protection for both of us.