MDF does work well, for at least two reasons: It's dead-flat and smooth straight from the shelf, and it's very firm. The lack of 'give' in that surface is a good thing, and is what helps to prevent rounding of the apex. MDF is particularly good for polishing tools requiring dead-flat bevels & backs, and perfectly straight edges, like wood chisels and plane blades. I use MDF for my wood chisels, with green compound. I generally avoid any surface that has much give, if it's used with compound. I occasionally use leather for stropping, but only without compound.
The one reservation I have with MDF is, when polishing with very small/fine-grit compounds, there may be some issues with coarser scratches in the finish due to embedded dirt/grit in the MDF itself, for which the manufacturing process is somewhat 'dirty'. But that's generally only a cosmetic issue anyway. I've occasionally used bare MDF for stropping/realigning edges on my pocketknives, which works pretty well, and I can sometimes see the extra scratches left by the grit in the material, on my bevels. Again, it's a cosmetic thing, but doesn't generally affect sharpness at any finish lower than maybe ~ 800-grit or so.
MDF is among the substrate options suggested by DMT, for use with their Dia-Paste and Dia-Spray compounds (quoted below, from DMT's site):