While this is common sense interpretation of the term, the whole idea raises some other tricky questions about how that chunk of apparently unused time way off in the future was arrived at, how confident anyone can be that it is really there at all and how the various parties to the contract will interpret it.
The matters of who, if anyone, is entitled to use it and what for and how that would be arranged etc etc is only part of the picture, perhaps not the most important, and cannot be considered in isolation.

The contractor doesn’t want to give it away or even show it to the client because he doesn’t have much confidence that it is really there, because it arises from very early planning at tender or contract stage. Further modeling, with more detail which picks up the scope more precisely, might well soak up the reserve. Even if the modeling is perfect at these early stages (it never is, but is often presented as or taken to be an ironclad promise), circumstances during execution will conspire to force or allow the contractor to use it up. Both parties know all this but pretend not to.

The contractor takes the schedule risk and that Terminal Float is just about his only way to mitigate the risk. He knows there is a risk and manages it partly by having a buffer for reserve.
A client would be working against his own interests if he undermined the contractor’s reserve by trying to either stuff some additional scope into the Terminal Float or trying to have it chopped off so that the contract finish date can be dragged to the left.
Even so, we know they try both.
So the contractor is better off hiding the Terminal Float by distributing it to Tasks on the Critical Path, squirreling it away. This is called padding, which is a whole other problem that Stephen Devaux has something to say about.