I by no means spend all day sawing stuff, but I always use one of those Irwin ryoba when I do, and sometimes it is plastic.
Most often I cut acrylic, and it blasts through that. With softer plastics, especially HDPE, binding is a bit more of an issue, and it’s harder work; I assume it would be better to have a different tooth pattern, but even if you can buy specialised Japanese hand saws for plastic, I doubt it’d be worth it.
One thing I would say is that every time I replace my saw, it’s not because it’s dull but because it has too many broken teeth. Cutting hard plastics is probably worse for that sort of thing – I’ve never cut polycarbonate, but if I did I would be careful to go slow.
