The strange thing is long term disability insurance for a group plan is really cheap. My work provides it as an option and I only pay $300/year or so for the premiums, work doesn't pay any percent of the premiums.
Adverse selection is a huge problem in insurance. And disability fraud is especially bad (like billions of dollars in CA every year).
As a result, insurance companies don't want to play in that space, since their average margin is only like 6% anyway. States backstop the insurance companies, to make sure they continue to offer the product.