Recitals in contracts are prima facie evidence that the facts recited in them are true. This could be relevant if trying to secure a default judgment, or if the party who signed the document is no longer available (e.g. due to the death of that person). In the absence of any other evidence, this should prevail.
In theory, the recital is also supposed to warn someone who is being pressured to do something not to sign it at all. As the analysis in the question makes clear, however, people acting involuntarily or under duress may rarely refrain from signing, despite the warning.
It also puts a notary or witness or counterparty to the contract on notice that they shouldn't allow someone to sign it if they appear to be acting involuntarily or under duress.
No catastrophic harm would occur if this phrase were omitted. It is part of a general strategy of defensive legal practice and doesn't hurt the client who is paying to have the contract drafted. It also helps make the agreement sound legal and official which may help the parties and a later court reviewing the parties actions to take it seriously and conclude that it really was intended to be a contract. The client who is paying the lawyer to draft the contact gets no benefit from having a contract that is one sentence shorter, but might get some slight benefit from including additional language.
And, sometimes putting seemingly obvious or stupid statements in a contract does work.
For example, one case I recall involved an employment contract that specifically said that: "It is outside the scope of your duties to assault or attack people or property." The employee then, in a fit of road rage while refueling a company vehicle while on the job sprayed someone else who had cut in front of him at the pump with fuel and set them on fire. The case against the employer for liability for the actions of its employee during the course of the employee's work for the employer was dismissed because the employment contract said that doing this wasn't part of the employee's duties. This is not the fact that I would have found important in resolving the case, but it convinced a judge after the fact.