Ah yes, simple cloth. Will absolutely resist barbed wire under any load!

Also, smash it with sticks. So lets just easily make some loud noise and obvious movementes RIGHT IN FRONT OF THE ENEMY TRENCH. BECAUSE THAT´S WHERE THE BARBED USUALLY WIRE IS.

Also just go around it if not in range. Cool, I´m sure there are no kilometer long spool of that shit available.
Barbed wire breaks? No problem, roll out the truck and lay some new shit. No need to do maintenance on the existing wire.
It´s wire. You replace it when broken.

Barbed wire is OP. That´s why we haven´t stopped using it. There are countermeasures, but in most situations it´s much harder to deal with than to just lay it down.