What we have seen has not been particularly private or high-level, and in that context it makes more sense to feign belief in ME being an easily curable mental health condition. Lower level employees are happier to discriminate against patients and brainwash our doctors when they truly believe they are in the right - much like lower-level CBT practitioners. True believers make much better sales pitches. So I think the efforts of White & Co are aimed at helping the insurance industry in numerous ways, and we really aren't seeing what's going on behind the scenes there sufficiently to know what their real goals and awareness are.
First, public perception makes it easier to deny claims by ME patients. Peter White and other insurance lackeys do a good job in that regard with all of their militant patient claims, news coverage of ME being curable with CBT, and general implications that ME is a self-inflicted psychological disorder. This can prejudice tribunals who are assessing denial appeals, politicians who opt not to intervene, and the general public not to get up in arms about unfair and repugnant practices.
Second, re-classification of ME/CFS can save the insurance industry a lot of money in claims. And the psychobabblers seem to have been pushing very heavily for this behind the scenes. There's already a nation-wide fatigue categories added to some version of the ICD, where "chronic fatigue" lacks a neurological classification, and is even explicitly applicable to and synonymous with CFS. There are also indications that a similar move is underway with the global ICD codes, to reclassify CFS at least in a less biomedical manner, and bring ME with it if possible.
And then we have new codes regarding Bodily Distress Disorder or similar MUS concepts, where anyone having more symptoms than someone thinks they should is presumed to have a mental disorder. Which opens the door for saying "sure, you have a neurological disease, but part or all of your disability is due to BDD and not ME itself, so no payout for you."
And as to why they don't just list ME/CFS as an exclusion: because insurers make money by offering insurance, not by excluding insurance before it's even been bought. It's simply bad marketing to say they'll insure people - unless they come down with something debilitating and incurable. Bait and switch requires that the bait be tempting enough to attract people to sign up, to collect their premiums for years or decades, and to replace the product with a shittier one only when it's too late for the customer to switch to a different insurer.
It would be interesting to know how much of the ICD and NICE debacles the insurance industry is behind. But I doubt we'll ever be able to find out. Most of that would be down to private transactions between the insurers and their employees. At best we know that the people aiming for psychologization of ME/CFS have insurance ties - but we will never know the orders they've been given from the top, or have proof that their actions are the direct results of their bosses orders. Though perhaps it's best to assume that their actions are in their paid capacity as employees of the insurance companies.
Personally I think any paycheck or other incentive received from insurers should disqualify the recipient's input in any government, regulatory, legal, or medical context. The conflict of interest isn't just potential - it's almost guaranteed that they will never act against the orders or best interests of their employers. Better safe than sorry, when it comes to public health.