My makerspace does not allow PC to be cut in the laser-cutter. The plastic smokes and catches fire easily. Smoke is very bad for a laser-cutter because it settles on the mirrors making them absorb the laser instead of reflecting it.
PC is sometimes laser-cut industrially though, but I think most firms do only sheets that are much thinner than what you would need for a plate.
So, likely, you would have to CNC-route it, which is more expensive, and you wouldn't get those clear, crisp edges that you would get with acrylic.
The plastic is also more expensive to begin with.