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- When to use RIndler coordinates or the principle of equivalence

Not sure when to use Rindler coordinates to analyze dynamics in a constant accelerating reference system. Rindler coordinates seem messy because they are always changing. Wouldn't it be easier to invoke the principle of equivalence and treat the environment of an accelerating system as a gravitational field? For example, suppose an observer in an accelerating frame with constant acceleration throws a ball at a 45 deg angle with respect to his system. According to this observer he will see the path of the ball as a parabola. With respect to an inertial observer wouldn't it be unnecessary complex to try and figure out the path the accelerating observer sees my using RIndler coordinates to determine this?