I've cut a lot of foam over the years. Pink foam from the big box store, White foam from the same place. High density foam for signs. It does make a mess. Before the ShopBot I ran a MultiCam that used a ball screw drive for the "Y" axis (25+ years ago). The foam would stick to the threads and build up until it stalled the CNC. With the ShopBot you have to watch the rack & pinion teeth for buildup. The machine attracts foam dust, pretty hard to catch it all, and sticks to everything.
These are all the cheap white Styrofoam that is one of the worst for static clinging. With these, I used a 1/2 inch drill bit. I bull nosed the end of the bit on the bench grinder. A drill bit has more than enough cutting edge to cut 2"+ foam with a single pass. Poor Man's Tooling.
BTW I should mention, the pipes in the harps below are 3/4" copper pipe. My son set one of them up with servos that struck the pipes and He hooked those up to his computer and played Christmas chimes for a Christmas display at Church.