I think it's not correct to hold this kind of physics to the standard of science that other disciplines use.
The standard, scientific method version of science is 'guess a model of how the world works, then run an experiment to see if it's true'. This packages (hides, even) a bunch of principles of rational thought inside of it - for instance, that a stance about how the world works had to be able to be wrong, and that you should be picking your opinions about how the world works based on what you can (repeatedly) demonstrate.
But there are other paths to knowledge- and revelation- gaining that are performed by scientists all the time, yet don't fit this model. It's perfectly legitimate to get a grant to run an experiment to just look at something closely, such as a star or a blank patch of sky, or a material, or an organism. 'I want to collect data on X' is perfectly legitimate as a way to learn about the world. After all you need observations about something in order to build the initial model that you use to generate hypotheses in the Scientific Method (tm) anyway. Another example: sometimes experiments are done just to find more accurate readings of numerical constants.
Anyway, mathematicians and the more theoretical physicists aren't really looking to run experiments to test hypotheses. Instead their 'experiments' are finding new models for looking at things and their 'results' are finding new mathematical statements, or finding ways to prove things that were previously hard to prove, or just finding new ways of looking at things that make thinking about them easier. This is 'output', and a net gain in human knowledge, without being a testable hypothesis, and I think that's fine. It's still subject to the underlying rationalism behind science. But validation is entirely theoretical: a good theory makes things make sense, and doesn't make things not make sense in ways that disagree with physical experiments, and makes things simpler and better. And it's fine that these criteria are abstract and to an extent subjective.
Of course it's still necessary to have a way to say if theorists are failing, or wasting their time, or producing too little or too quality output, and I don't know how that's done or it ought to be done. But it doesn't bother me that they don't produce physically testable results.