I see what you are saying, but to each his own: I’m one of those kids (there's one in every mechanics class) that grow irate at the sin(ϴ︎)≈︎ϴ︎ approximation in the pendulum solution and then waste weeks using the full series expansion, only to find out the results differ only in the third or fourth decimal place. The thing is, I emerged from the experience thinking to myself “that was a useful learning moment”.