It won’t be their premiums going up: if you rear-end someone, you’re at fault.

That is logically correct, but it’s not how insurance companies think.

That would be a better bill: insurance cannot consider incidents one isn't at fault for when determining a rate. Absolute scumbags.

Scumbaggery of insurance companies aside, if someone gets into ten accidents a year where they're deemed not at fault, I would still be very skeptical of that person as a driver. I would not find it immoral to apply higher rates in that situation.

If they are so reckless there would surely be a better signal alongside that one?

On some weird level actually insurances of the more expensive to repair or more often to repaired cars should go up. Even if their insurance is not paying for damage. This would be due to those cars affecting the outgoing costs.

So if your car is expensive to repair, it should have higher liability part. As on population level it has higher cost for other insurances.