Externalities on future generations?!

It is often said that the GHG emissions of the present generation have negative externalities for future generations, or also, that they involve costs for future generations. That is: While the present generation reaps the benefits associated with emissions, it externalizes the costs of these emissions to the future.

I want to argue that there is something problematic about the idea of "externalities" or "costs" to future generations. I assume that the concepts of "cost" and "externality" are understood in the sense that an action of A counts as imposing an externality/cost on B in case B is made worse off than it would otherwise be, i.e. had the action not occurred. So, if A listens to loud music this imposes an externality/cost on B because B is made worse off than if A had not listened to loud music. In such simple cases, it is clear which two situations are compared: The baseline case is the situation where A does not listen to loud music and the deviating case which is said to involve costs/externalities is the situation where A does listen to loud music. A's not acting (i.e. not listening to loud music) is the case relative to which we compare other cases and which helps us separate costs from benefits (or, respectively, negative from positive externalities).

The problem in the intergenerational case is that we do not have an obvious baseline scenario which would allow us to separate positive from negative externalities (or, respectively, costs from benefits). If someone claimed that global emissions of 30 billion tons involve negative externalities on future generations, we can always ask: Relative to what baseline is the future generation made worse off by these 30 billion tons? And why is this the obvious baseline? Would you count global emissions of 5 billion tons or of 0 billion tons (or of -2 billion tons) as positive externalities or would you still count them as negative externalities?
Similarly, we can ask how much the present generation has to save for those savings to count as a positive externality. Does any addition to what the present generation has inherited from past generations count as a positive externality? And, if so, why? Why should zero savings be the natural baseline relative to which saving more counts as a positive externality and saving less counts as a negative externality?

In the non-intergenerational case, we are in possession of an obvious baseline: "Not listening to music" - or more generally: not doing something, not affecting the world, leaving the world as it is, in its status quo position. In the intergenerational case, we are not in possession of some "status quo" of future generations (associated with not acting on our part, i.e. not affecting future generations) relative to which we could count worsenings as costs and improvements as benefits.

So, there is something problematic about the claim that GHG emissions involve externalities or costs for future generations.

(P.S.: Some more things would have to be said, e.g.: (i) that I left the Non-Identity Problem out of the picture or (ii) that in some cases context makes it obvious what counts as the baseline or (iii) that there actually is at least one salient baseline: the baseline of what we owe to future generations).