The short and easy answer is: money.
Most Long Term Disability ("LTD") insurance plans have terms that reduce the amount of money paid each month if the disabled or injured policy holder get Federal Social Security benefits. Furthermore, the medical treatment the disabled worker may receive can lead to a reduction in their symptoms such that they can go back to part time or light duty work, further reducing the amount of money the LTD insurance company may have to pay.
The LTD insurance companies also save money when they deny claims. If the Social Security doctor finds reasons to deny the disability claim, the LTD insurance claims reviewers can use this evidence against the injured worker. And, since the private insurance company did not have to pay for the Federal Government’s expert medical witness, they get a "free" report and opinion to support their denial of the claim. Lastly, they pay nothing for the several levels a Social Security Application for benefits goes through, and many such private LTD insurance policies state that if the insured does NOT apply for Social Security, they can lose the Long Term Disability benefits, even though they paid the premiums for that protection! These are the reasons that many private LTD insurance plans require that the disabled beneficiary apply for Federal Social Security Disability Income ("SSDI") benefits.