When the mithril 2-hander is equipped you can't slash webs. I don't know about the other metals, but I'll test the other 2-handers. Anything with a sharp blade should cut those webs. Keep your swords sharp! ;)
Turns out this is for all 2h's, I just tested. Will report this to the devs, thanks for the report!
Reference: blitz/core-engine#137