There are lots of diseases which are not diagnosed by a blood test or imaging. They are diagnosed on the basis of clinical symptoms by someone with medical expertise.
This does not mean they are not 'unequivocally diagnosable'.
My family member has a rare form of motor neuron disease which was unequivocally diagnosed by a national specialist 3 years ago. She's now near to the point of death, her lungs are packing up, she started with one leg which suddenly stopped working properly, then it spread.
There is still nothing which would show up on a scan or blood test - but she most certainly is dying from the disease with which she was unequivocally diagnosed. Are you saying she shouldn't be entitled to her hospice care because she might be faking it due to a lack of evidence?
A private ADHD test costs a fortune - so I'm not sure who these people are who are paying for a private ADHD diagnosis so they can claim some meagre benefit payments.
NHS waiting lists are clogged up with people who might have ADHD, not people who want to claim benefits. It's a 3 year wait for a child and a 10 year wait for an adult diagnosis - that's a pretty long-term strategy for lazy people looking for fraudulent benefits claims.
Also the ability for some people to get a private diagnosis means there are less people on the NHS waiting lists - it's unfair thar some people can access private assessment and some can't, but it wouldn't make those NHS waiting lists shorter if private assessment wasn't available.
Your logic is heavily flawed.