The problem with that is the same as we would get if we decided that the way to treat anorexia is by allowing the patients to starve themselves to death. They would die thin and happy, but I don't think many people would agree with it being the "preferred solution to that problem".

You're comparing apples and oranges though. We know that anorexia can generally be treated with cognitive therapy and help restore people to a healthy and comfortable body weight. Those same treatments fail when applied to people with BIID. And they way they cause harm is different as well, since failing to treat anorexia results in starvation. While refusing to treat BIID results in people taking dangerous risks to amputate themselves.

I don't see much of an actual solution to these issues in your arguments other than some hand waving about politics as some sort of root cause.

I fail to see the parallel. Anorexia as "starving themselves to death" is not a stable identity, it is an identity in decline with ongoing suffering and temporary highs.

Should taking of legs be the first treatment option? No.

Should people get therapy, medication and other treatment? Yes.

Should those treatments be refined and improved, sufferers of BIID experimented on to improve treatments? Yes.

If society is unable to come up with a treatment that works for years should society deny sufferers this radical treatment forever? No. That is imposing the majority world view on a minority when the difference in world view poses no harm. Yes, society would need to address potential cognito hazards/memes and make sure there are no people doing this for economic incentives or other mental illnesses for which treatments exists.

If society would let people get the treatment, that would not be capitulation. That would be acknowledging that while society has interest in being able to treat that, that interest can not forever outweigh the benefits the radical operation has for the sufferer. Capitulation would be if society stops trying to find a treatment besides radical operation and handed operations out without scrutiny.

How does one distinguish between a stable identity and an identity in decline?

One way to do that would be to look at outcomes of patients who have received the therapy to see if they feel their needs are met, like this study did.