Do I need two sets of dishes?

Hi Rabbi!

Could you clarify a bit further about needing two sets of dishes? If glass/corelle/glazed dishes do not need to be kashered (Laws of Koshering (Hag’alah and Libun)) why wouldn’t we be able to switch off using the same dishes for milk and meat as long as they are clean in between uses? Is there some other reason the Halacha says to have two separate sets of dishes?

I inherited one set of glass dishes used for both milk and meat for Pesach (that’s how I grew up). They haven’t been used since last Pesach. If, indeed, we can’t share the dishes for both meat and dairy, can we at least dedicate the existing glass dishes that were previously used for both to be for one or the other?

Thank you so much!