Goats will just stand on this, or rub against it, until they can nonchalantly walk over it. Trust me! I've seen it in some places, but this is where the goats had ACRES of brush to occupy them and were in a large group, which means less chance of boredom.
And strands of barb wire are not going to work; the goats will just squeeze between it, possibly causing severe injury to a delicate udder or underbelly, or even becoming tangled. Barb wire along the top of a fence may help, but it may not. Also, with hotwire, goats quickly learn the "pulses" some brands use and slip between them. They are as intelligent as most dogs.