A few thoughts regarding chase tours (regardless of motivation and behavior)
Regarding insurance:
From a coverage aspect, it seems prudent to have a full-disclosure "come to Jesus" discussion with your insurer so they are well-informed of the conditions you will be chasing in, and they are aware it is a COMMERCIAL, FOR-PROFIT endeavor with paying passengers. It is at this point that 95 percent of insurance companies who do not employ actual underwriters will decline coverage. Once you have discussed these things with a company that is willing to underwrite you (Lloyd's of London, perhaps), you will find they will offer a highly restricted policy that costs a literal fortune per year, and it will be filled with exclusions/conditions such that the insurance company is favored in nearly any situation and can therefore find ways to deny a catastrophic claim. Insurance companies are FOR-PROFIT businesses and have an entire fleet of lawyers at their disposal. They simply will not risk $150K+ liability per passenger plus likely vehicle damage for a premium most tour companies can afford.
Because of this, I speculate there are a lot of pop-up chase tours that only have typical personal insurance coverage on their vehicles, with their "business model" relying on a combination of luck, insurance company deception "I was jus' drivin' down the road, and... HAIL!" and the relative comfort of having signed waivers from their customers (more on this in a bit).
Regarding liability waivers:
I am not a lawyer, but I don't have to be to initiate litigation
Even the most iron-clad waiver can be shredded under certain circumstances, and I chuckle to think how many tour operators took the cheap route and used a boilerplate waiver they found on the internet rather than engaged an attorney to write one. That being said - A customer can sign a waiver that states they understand chasing is inherently dangerous and that they may be placed in dangerous situations the tour company cannot predict or control, but the tour company would STILL be expected to engage in best practices when presented with choices and not act in a reckless or negligent manner.
Practical example:
Getting in an accident while driving 100mph or running a stop sign to get to a storm: Likely not able to be waived (it's hard to say you're acting in a non-reckless manner when you're breaking the law.)
Reasonable exception: Driving 100mph or running a stop sign because OMG THAT TORNADO IS GOING TO KILL US, might be considered part of the "inherently dangerous" nature of storm chasing.
Perhaps ironically, any litigation from an injury accident it would be highly documented because nearly everyone involved (including the tour operator) has unbiased video documentation. This would include video of any speeding, running stop signs, driving faster than conditions/visibility would warrant, decisions to drive through a hail core rather than take safer, alternative routes... And tapes would be played to a jury from the beginning in an attempt to show patterns of reckless behavior. If you have NEVER made a questionable pass on the highway or gone more that 5 over the speed limit on an active chase, you are definitely in the minority. I sure wouldn't want to face that sort of scrutiny.