Without tests it’s just pretty math that can be coaxed into agreeing with reality but that proves nothing.
Physicists try to indirectly test all the time via cosmological observations but that is extremely hard and limited to what you can infer and how well you can eliminate other explanations or sources of error.
If it is competing against another model that does both that and offers new testable hypothesis (which experiments match), the other model is the clear winner. But lacking that, if no other model explains all existing data, is new testability really necessary when it is the only model that currently explains all existing tests?
That said, aren't most of theoretical models only contenders for such, as in they haven't been expanded to actually explain all testing results, only that, as far as they have been expanded, there are no contradictions yet? So they need physicists to expand them, but if the model is wrong, the effort might largely be wasted, and we have some models that there is disdain for not because they contradict existing experiments, but because they have eaten too many careers without showing value in return?