I think:

Toss a coin. Either a buyer would want it or wouldn't want it.

As for improving value, absolutely no. Temporary buildings (those built
without a foundation) add nothing to the appraisal of a house, and it is a
matter of argument with a buyer as to whether they add anything to the
price. Yah, like you want to argue with a potential buyer.

You will recoup nowhere near the cost of the shed unless you find a buyer
who wants it for an outbuilding or shop. That, in my experience, isn't most
buyers.

And buy your wife some Dockers if she wants to be the man of the house.

Steve