That makes it a whole different game, yes. By casting it in sections you avoid adding a lot of pieces that you would have to laboriously add when cutting the plate as a whole.
The site I linked to (mainly because it was the first one I found) sells laser cutters suitable for plastic sheet that avoid this problem. Here’s an example from that site:
OK, these are industrial machines, but with a bit of luck, there are hobbyist-scale ones to be found with similar capabilities.
I think you’re confusing polystyrene in general with expanded polystyrene foam. Nearly all model kits are made of hard polystyrene, as is the kind of (usually white) plastic sheet/card most commonly used for scratchbuilding.
I also get that feeling after drawing something intricate
But that’s the beauty of modelling and scratchbuilding, IMHO: you can build it the way you think works best, and I can get much the same result via another technique. Does that make either better than the other?