I built a storage box under my PM3520 when I got it ~15yrs ago. The bottom ~6" has a false bottom storage area where I initially loaded 300lb+ iron to add mass to the lathe. After experimenting with large, out of round, logs I determined that that additional mass only changed the speed I could run before wobble by about 10% (ie from 400rpm to 440rpm). Based on this I choose not to move that dead weight when we relocated to TN, and that slight improvement is not missed; in fact, 95% of the time I don't even lower the rubber feet to take it off of the castors.
Even with the doors, I still collect dust and shavings inside and have to blow it out once in a while (obviously haven't done that for a while). The backside also has an access door like the front, but I rarely (never) use it. I really like the tool rest storage holes on the left, and the simple gouge holder on the right (glued 3 open pvc pipes together - easy to lift out and blow out shavings *each* time I sweep) that keeps 3 tools handy when using. Also, it's imperative that it's up off of the floor to allow easy sweeping. I added a 90deg 'roof' deflector (white melamine) after using it for a while and having to clean off the top from shavings that drop between the ways.