Do you really need separate milchik/felishik pots?

Question

Dear R' Abadi, In reading over your tshuvot, it seem like you can cook a pareve item in an aino ben yomo pot that is fleishik and then eat or cook that pareve item with milchiks (or vice versa, l'chatchilah. If that is true, do we really need separate pots? Other than not wanting to wait 24 hrs between cooking meat/milk or a geder around confusion or social norms, is there a halachic reason to have 2 sets? Much thanks. best, Simon