MDF is made of small fibres held together by a huge mass of glue. For an instrument to sound 'good', the body woods need to transfer vibrations/soundwaves well. With MDF being formed of so many small fibres, and glue being amazingly poor at transmitting said soundwaves, it does not lend itself to musical instrument making well. Neither does plywood, although it has fewer pieces (just the number of sheets in the ply), the differing grain directions would cause the same sort of transfer problems as with the fibres of MDF.
It's not a case of snobbery that they are cheap, they just aren't usually considered good enough (there's a reason why even the cheapest guitars these days never use plywood). Aesthetics aside, they're pretty much functionally inadequate.
You'll do much better (as was suggested above), to buy a cheap hardwood like Alder/Ash for your project.
←