With modern chains I don't think it's likely that a chain will break. But if I would be thinking about removing the chainguard, I would make sure that neither me nor the passenger would ever wear wide trouser legs, and that the shoelaces are always tucked in.
In any case, I like the looks of chainguards. I rather keep it than get rid of it, even if it is only for the looks factor. The same goes with front fenders. I rather have one, even if it's minimal, than getting rid of it.