It seems like you want to load the verb with the judgemental aspect, but the context is always going to be that the making is in itself succesful and therefore positive, even if the product made is not going to be wanted. Because of this you are not going to find one word that does the trick. Two words is easier:
Originator of tat / purveyor of tat.
There is a verb "to mangle" which can be used in the context of "to mangle a tune" which is making a noise nobody wants.
Proliferating redundancy and breeding degeneracy?
There are words that can refer to the thing nobody wants: gimcrack refers to something that is made but is of little value and has a quite negative context:
Tat is an English word meaning things made of low quatlity, which is often used in the context of stuff that is new but nobody would want - there are lots of shops on English high streets that sell gifts and memorabilia, and most of this is referred to as pointless tat.
In respect of the making part then "mocking up", "faking up", "bodging", "cobbling together", could all refer in a negative connotation to making stuff nobody would want: e.g. "cobbled together a load of tat".
But none of these match the pure phrase you are looking for. Inherent in the question is a contradiction, because if someone makes something then at least one person wants it, otherwise they would not have made it. If there are these kinds of semantic conradictions then it is not possible to find one word to cover both sides of the contradiction.
If it is in terms of a more passive type of making such as "making" babies, then there might be some verbs appropriate to that.
An important factor is whether or not there is a negative or positive connotation. For instance, if someone is making face masks in order to prevent infection then you could say these were things that were made that nobody wants to see, or to think about, but would that necessarily have a negative connotation? Of course nobody wants to be infected, so the fact they don't want to be used would connotate a positive outcome which the grammar would respond to, and so there is unlikely to be one word that can be used, there will always be a defining context and this will require extra words to set that context.