You need to convince not me, but people who are good at writing grant proposals and passing ethics boards :-/

Sure, but I have now managed to convince myself, so I am practising. Please be the most evil opponent you can be!

Second, consider the incentives.

Incentives-wise, doctors are regularly getting struck off for believing and practising this, all over the world. And the NICE guidelines specifically say that thyroxine is not to be used for the treatment of CFS. You'd think they'd be overjoyed to have a reference to quote when striking people off/writing guidelines.

Would you be terribly interested in writing up "we tried a weird thing and ended up killing some people" results?

Well, I think that's exactly what the Scottish GPs thought they were writing up! They found 'no difference from placebo' in their patient group, and 'harmful' in their control group.

Where we differ is that I think that means that they must actually have done a fair bit of good in their patient group (specifically, in that portion of their patient group who actually had type 2 hypothyroidism, and for whom 100mg thyroxine/day was roughly the right amount. According to Skinner, that would have been too much for many of them, and too little for many others).