I looks to me that only the bottom right three cabinets have doors. In which case I would say forget about face frames, make them euro-front style, and put hardwood moulding on the edges of all the exposed front edges of the shelves.
In my limted experience with MDF (mostly using it for countertops that were then covered in laminate, but I did make one set of shelves) I found that it could take a nice finish, but as often as I got a nice clean edge, I managed faint saw marks. It also seemed mostly unsandable, so if it isn't machined clean, it will be hard to finish. I think I understand your intention is to cut out the face frame from a solid piece, which would require cutting out a closed interior square/rectange, in which case I still think it would be very challenging to get clean inside cuts.
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