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I certainly would not, as you would be more restricted in your freedom to communicate and opening yourself up to more possibilities of legal troubles down the road.

They would love it if you signed, but I can't see any benefit in it for you.

If they are pestering you, the NO, definitely not. Why would you sign something at this point? You already quit.

Cost/benefit? What's the cost, and what's the benefit?

From your description, it appears they are asking you to take on a "cost" with no corresponding benefit. Fail.

If/As you are under no legal obligation to do so, why do so? Is there some professional, relationship, or other benefit to doing so that you've not yet described here?