I don't have a ton of experience in E&O, but I do work in insurance and I don't think this is right. Buying a policy to file a claim for an event that already happened is called fraud, and while it does happen, it's generally pretty easy for insurers to detect and prevent.
In general the advantage of claims-made policies from an insurer's perspective is that they don't have to hold incurred but not reported (IBNR) reserves after the policy term. With an occurrence-basis policy on a relatively long-tailed line like E&O, the insurer generally needs to hold IBNR for several years after the end of the policy term. It's expensive to lock up capital for that long - as the insured you effectively pay for that capital (through higher premiums) at the insurer's cost of equity, generally upwards of 10% annualized for stock insurers.
Obviously the insurer's tail risk is also lower for a claims-made policy, but that's less of a factor at scale since it's diversifiable. (Or at least mostly diversifiable - there might be some contagion risk.)
In general the advantage of claims-made policies from an insurer's perspective is that they don't have to hold incurred but not reported (IBNR) reserves after the policy term. With an occurrence-basis policy on a relatively long-tailed line like E&O, the insurer generally needs to hold IBNR for several years after the end of the policy term. It's expensive to lock up capital for that long - as the insured you effectively pay for that capital (through higher premiums) at the insurer's cost of equity, generally upwards of 10% annualized for stock insurers.
Obviously the insurer's tail risk is also lower for a claims-made policy, but that's less of a factor at scale since it's diversifiable. (Or at least mostly diversifiable - there might be some contagion risk.)