The costs of weeding out the capable are high. Not just financially; you have to interview and assess people who might have severe and enduring mental illness and who might be very anxious about that interview and assessment process.

Unfortunately at the moment the assessment, while with a real doctor, is merely a box ticking assessment. You turn up in a clean shirt and tie (because you have a crippling OCD)? You don't get points. You turn up unshaved, unshowered, in an unclean t-shirt? You get points. At the end someone adds up all the points you get. If you get more than X (for physical problems) or more than Y (for MH problems) you get the money, otherwise you're fit to work.

Very many people who are deemed fit to work go on to win their appeals.

And that's the fundamental problem.

Is a wheelchair user able to work? Obviously, yes, there are many jobs someone in a wheelchair can do. Is a person who is totally blind able to work? Again, yes, there are many jobs that person could do. It's the same for people with mental illness; they might be able to work in a quiet office but not do anything customer-facing. The might be able to do many jobs, but need a bit of help to get those jobs.

Moving people off disability (disabled and not working; (we also have "cover extra costs of living because you're disabled benefits which get paid if you're in work or not)) benefits probably just moves them onto different benefits. They might still qualify for housing benefit and tax credits; the person caring for them might qualify for carer's benefit; etc.

Benefits and Tax in the UK is a mess. :-(