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- If Lorentz invariance is a special case of general covariance, why are all laws of physics required to have Lorentz invariance instead of general covariance which is more general?

All physical laws have to be Lorentz invariant according to a lecture I just watched. Why is general covariance (which is more general than Lorentz invariance) not a requirement for all laws of physics? Are there any quantum gravity theories that take the approach of adding general covariance to quantum field theory? Please recommend sources if there are any.