That is a clue as MDF has a lot more glue in its composition. Diode lasers choke on that. Same with plastic except the wavelength of the diode (blue) just passes through the clear whereas clear is opaque to a CO2 so the cuts are good.I watched some videos on air assist and the guy was using a CO2 on 3/4" MDF. It cut very clean and fast, quite impressive!
If you get tapering, I'd bet if you scored a lens with a wider in-focus range you could do thicker with out the taper.