Wooden mudguards

Gilles Berthoud are stainless steel.
I fail to see how they would end up tangled in your wheel. They are securely attached, have compound curves and decent stays.
Plastic ones deteriorate in sunlight and eventually fall to bits

I've got some vintage aluminium ones I must polish up. They would look amazing. And not be heavy.

They're what I have.

Been running them for, erm... 2 years now I think.

Never had anything stuck in them, the curve comes around far enough that nothing straight (a stick) could get in there. But if such a thing happened, then I'm pretty sure the only effect will be that it brakes half-suddenly. My bike is rear heavy (Rohloff), so I doubt it's going to kick me over the handlebars even if such an extremely rare thing happened.

Very happy with the Gilles.