Here we go again
The original IR35 looked like the End of the World As We Know It. But then people who were familiar with this area of tax and employment law pointed out that Inland Revenue (as they were then) had a consistent record of failure when trying to prove employment status. And so it transpired: you can count HMRC's IR35 successes in the intervening 20 years without taking your shoes off.
It's a measure of the value of contractors to UK business that IR35 was absorbed without disruption. The new rules will probably be similarly accommodated. Most companies that hire contractors don't do so because they can save on the tax bill, but because they can avoid long-term commitment or because it's the only way to obtain rare skills. They won't like paying more, but their needs remain the same, so they'll either just increase rates or, more likely, devise a set of arrangements that satisfies the new requirements.