It is also useful for a lot of practical problems, where you can treat ℏ as being essentially zero and c0 as being essentially infinite. If you want to get anywhere with any practical problem (like calculating how long a car will take to come to a stop), half of the job is to know which approximations (“cheats”) are okay to use. If you want to solve the fully generalized problem (for a car near the Planck units or something), you will find that you would need a theory of everything (that is quantum mechanics plus general relativity) to do so and we don’t have that.
It is also useful for a lot of practical problems, where you can treat ℏ as being essentially zero and c0 as being essentially infinite. If you want to get anywhere with any practical problem (like calculating how long a car will take to come to a stop), half of the job is to know which approximations (“cheats”) are okay to use. If you want to solve the fully generalized problem (for a car near the Planck units or something), you will find that you would need a theory of everything (that is quantum mechanics plus general relativity) to do so and we don’t have that.