It is extremely difficult to prove that something does not exist, depending on your definition of 'proof'. If you assume that 'proof' is 100% certainty then logically, nothing can be proved to be extinct. If you have a more realistic understanding of proof where there are degrees or levels of certainty then you can be extremely confident that something does not exist. I am highly confident that leprechauns do not exist. As you say, If I wanted to prove 100% that they do not exist I would have to look in 100% of the possible places a leprechaun could hide, in the case of a magic thing-a-ma-bob like a leprechaun, it would be the entire universe and more. I'm not likely to be able to do that, versatile as I am, so I cannot prove the non-existence of leprechauns.
We can be quite certain however that the huge clade which contains the dinos, aside from birds, is extinct. We could be wrong but that chance is quite small.
In any case it doesn't lend anything to creationists who through their arrogance believe a single sighting of a dinosaur would disprove all of the ToE and its many tenets.