Alex, don't feel as if the weight of the burden of proof (of concept generalization) has to rest completely on your shoulders. I realize you already agree that curiousity and your own interest can be enough reason to pursue a topic or generalization, but...
Isn't it the same as asking a question on mathoverflow about a topic which is interesting to you on its own merits, and finding out about the existence of either a longer history of it based on a parallel set of definitions or other possible applications of it in other branches of mathematics or physics? I had been working on a particular topic, but having approached it from one direction I could only perceive the question from my point of view.
Even my attempts to research it found nothing initially because I was using the wrong key-words to look for similar work on my topic. It turned out that there was a long history of work on the topic using different terminology which I had not been aware of.
Perhaps giving a short summary on mathoverflow (as a different question) of the generalization which you are working on would provide you some different points of view from other mathematicians.
As to the utility of a generalization or of a particular approach, it is not possible to predict or find all of, many of, or even more than a few of, the possible applications of a mathematical technique on your own because you cannot survey the entirety of it yourself. It's often the intersection of multiple disparate interests that creates the application of a technique onto a problem, and every individual (and every individual mathematician) has a different set of disparate interests. (As long as the number of categories of possible interests is greater than the logarithm in base two of the size of the population under consideration; otherwise the pigeonhole principle requires that there must be at least two individuals with exactly the same interests. :) )