Limits is one of the key underlying concepts we introduce at A level - exploring them and asymptotes in graphical representations helps ensure calculus and later topics link together? Exploring graphs of functions before differentiation feels valuable rather than just going straight into polynomials

We don't do limits formally, though. I'm not saying that's a bad thing (it isn't), just that since we don't do limits formally then it's a bit rich to claim that we do differentiation properly.