Maybe for the same reason my AME, who lives for aviation and pilots, stopped doing Basic Med exams. In his words, everyone coming to him for Basic Med had an issue with getting a 3rd Class.
Sure, there are some folks who do it just because they hate the FAA, but even around here, the advice to go on Basic Med is often given to people from whom obtaining a 3rd Class would be difficult or impossible. That could be for reasons that we consider arbitrary or capricious, but how's an insurance company going to distinguish between the pilot who just hates the FAA from the pilot who hunts down a DOT clinic where the doc doesn't know or care what conditions the FAA considers disqualifying?
We've even had discussions here about how conditions that disqualify you from a 3rd Class don't necessarily disqualify you from Basic Med. The insurance companies know that too. You're going to say it doesn't matter because those conditions don't make you any less safe to operate. But you (and the insurance company) don't know that for every such condition, nor do you know which condition(s) every Basic Med holder has.
Insurance is risk transfer in exchange for a premium. The insurer gets to set the terms on which it will accept the risk. The insured gets to decide if those terms are better than self insuring. Pilots who complain that a lack of insurance is keeping them on the ground are really saying they're unwilling or unable to meet the insurance company's terms AND are unwilling or unable to self insure on better terms.