I can't speak for all Libertarians and I'm not one myself - so don't take this as a blanket statement but, from my impression, a lot of Libertarians in the US support private alternatives to public services and private services as a first line of treatment.

Advocating that IP claims should be forced to fail in private arbitration before being eligible for a hearing in public court is a reasonable way to prioritize the private market fixing problems on the cheap before consuming public resources - but removing the courts as the ultimate arbiter is a really big shift in my mind.