This isn’t an incorrect approximation. It’s exactly how relativity was taught in my upper division physics class in college. General relativity basically start

This isn’t an incorrect approximation. It’s exactly how relativity was taught in my upper division physics class in college. General relativity basically starts with the assumption that everyone is moving through space-time at the speed of light. We sedentary material beings experience that mostly as moving through the dimension of time. Non material things like photons experience it as moving through space (because they lack inertia). When you accelerate to high speeds, you’re somewhere between the two extremes.