The point in contention isn't that infinities can be imagined, it is whether they are useful - specifically in the context of cosmology.
Numbers are clearly useful, otherwise it would be difficult to explain the importance we ascribe to the value of our bank balances. However just because you can formulate a model of reality including infinities it does not therefore follow that this model must be useful, or that infinities must be useful.
"The point in contention isn't that infinities can be imagined, it is whether they are useful - specifically in the context of cosmology."
Going the other way may be more useful; is it possible to create a correct model of reality that does not at any point use infinities? You could have alternate correct models that do, but if you can create one without them you'd have a reasonable basis to call the infinities in the other models unnecessary and nonexistent.
(I would suggest before anyone rush to correct me that they read what I said carefully. For instance, "reasonable basis" != "undeniable proof", which experience leads me to believe is a difference a hypothetical replier might, in their rush to reply, overlook. Also note the two clauses in the question; if it is simply impossible to create a correct model of reality at all, we may never get to the "infinity" portion of the question.)
usefulness is a pragmatic attribute, it does not by itself say that something really exist in reality, unless you believe that everything that is useful exists. I think the OP do not believe that everything that is useful exists in physical reality, therefore seeing four tables does not mean that fours exists in physical reality separated from tables or other objects. So you are probably using different metaphysics..
But sure, since the days of William of Occam pragmatic metaphysics have been popular, but again popularity does not necessary prove something is right. Just explaining both sides of the argument here and trying to resolve the potential missunderstandings
Of course "they" do - just like anything you care to use a word for, e.g. "humans." All words are, in fact, abstractions, and these abstractions do exist in a meaningful sense.
Numbers are clearly useful, otherwise it would be difficult to explain the importance we ascribe to the value of our bank balances. However just because you can formulate a model of reality including infinities it does not therefore follow that this model must be useful, or that infinities must be useful.