Contracts in general do not need to be in writing. That is true in general. There are certain categories of contracts that must be in writing in order to be enforceable, but even though a contract may be enforceable, it’s still best if it is in writing.
The reason why is writing makes very clear in most cases what the terms of the contract are. If you have an oral agreement, that is very susceptible to people having different memories of what the agreement was exactly. There’s nothing quite like a written agreement to clarify what the terms of the contract are.