How can cutting the premiums of safe drivers work in practice?
They would raise the premiums of bad drivers, or just not accept the bad drivers as customers.
Isn't the idea of insurance that the premiums of those who don't file claims is what pays for the claims of others?
Yes, but that's after taking all predictable differences into account. Even if you are a safe driver, you'll sometimes have accidents just because of bad luck, or accidents caused by others who are uninsured and won't pay for them, or whatever. The other drivers who didn't have the bad luck will pay for you.
Insurance isn't to allow people who engage in risky behaviour to transfer their costs to others.