Users should be given a choice and clearly and concisely explain the consequences of choosing one or the other. Simple as that.

What it should definitely not happen is to do this behind scenes and store recovery codes on a microsoft account. Why those codes have to be stored on their servers?

A screen should display the recovery codes and instruct the user to print them and keep them in a safe place in case of requiring them. I should be able to recover my data completely offline. End of the story.