That doesn't sound like a fair description. Physics doesn't simply assume symmetries exist. We've observed symmetries that hold up under all observational and experimental scenarios available to us. From that, it's quite reasonable to consider the possibility that those symmetries are truly universal, and to study models that treat those symmetries as universal. Those models have great predictive power for ordinary scenarios of the sort where we know from experience that the symmetries do hold up, and those models tend to be simpler than ones that break symmetry in exotic scenarios. When we actually find a broken symmetry (eg. space, time and momentum behaving oddly at speeds close to c), it's time to update those models, which then usually reveals a more subtle symmetry and conservation law.

But there's no big trend in physics that casts doubts on all the important symmetries in physics. Even under as-yet undiscovered theories, the symmetries we're familiar with will always remain true in the limit as the conditions approach familiar everyday circumstances. Nobody is worried that concepts like time, charge, momentum, etc. will be discovered to be a silly, unfounded idea that the universe casually disregards. We're just not adding extra terms to the equations until there's a need for them.