There have been several styrofoam panel speakers made. There were a bunch of low end noise makers who stuck the magnet/voice coil motor structure on styrofoam panels, but the first from an actual named audio company may have been the Yamaha ear shaped speakers (which I lust to own), which were assymetrically shaped to surpress resonances, but which the marketing firm decided should claim that they were shaped like ears because that is the best shape for speakers. Which sounded ridiculous.
A bigger problem was that they were dipoles, at a time when dipoles were almost unknown (the Quad Electrostatic and the Wharfedale SFBs were the only ones I know of, and neither had much market penetration). This is a problem that also beset the BES range.
The next styrofoam panel speakers I'm aware of of were the Fisher Sound Panels (which I think were made by BES). They were in nice frames and had grills made to look like paintings, and were made to be hung on walls. I have no idea what was supposed to happen to the back wave, but I was surprised at how good a pair brought to an early Frankenfest sounded.
Then came the Bertagnis, which were much bigger, so had the potential to make serious bass if positioned correctly. But speakers out in the middle of the room have never been popular. and I suspect customers weren't prepared for how persnickety dipoles are about positioning. So they came out with considerable fanfare, but didn't seem to sell well.
There is also the problem with styrofoam's significant resonance at around 400 Hz. The two best known drivers that used styrofoam in their structures - the Leak Sandwich and the KEF B 139 both had a layer of aluminum foil laminated to the front to dampen that resonance - I think the Yamaha may have also had it. I've had a couple of Phase Techs that used a different black foam, bonded with some of the most persistent goop ever, which I assume did the same thing. (And now that I think of it, I think there some Sony APMs that also had damping foil.)
I suspect the BES speakers did also - if they didn't, that might go some distance to explaining their lack of success. My memory of the el cheapo styrofoam speakers noted at the beginning of my post is that they had nothing of the the sort, which is why they were cheap, but also why they didn't sound very good.