Why do I need phase margin if I know the transfer function?
Well they are margins, as in a margin to (possibly) becoming unstable. Having the calculated transfer function being stable with a very small margin means that any change (or error) in your model or controller will mean that that stable transfer function will probably only be stable in your calculations.

Try reading about it in Chapter 10 of Feedback Systems: An Introduction for Scientists and Engineers, they answer your question on their first phrase


  In practice it is not enough that a system is stable. There must also be some margins of stability that describe how far from instability the system is and its robustness to perturbations