The idea behind core competency interviews is to see whether the candidate has evidence of the skills needed for the particular job. And to do that in a fair way.
So if the job is say, a shop manager, they are going to deal with staff recruitment and staff management, budgets, complaints, health & safety, theft. That sort of thing. So you identify the general heading for each area required and then ask for examples of situations where they have managed budgets or dealt with fraud & theft, and where they have dealt with aggressive customers and staff. Where they had to tackle an equality issue. And so on.
Driving a train requires a different set of skills, but the principal is the same.
In the olden days people were often asked what they would do if they were Prime Minister for the day, or about climbing Ben Nevis for charity on a monocycle (as per their CV). All very entertaining but probably of no relevance to the work the candidate is to undertake. (Having said that, for some jobs, climbing Ben Nevis for charity might in fact bring in some relevant skills, for some jobs, if you used it effectively. Organizational skills, sound judgment, health & safety, good time keeping. There’s potential there).
You were obviously unhappy about the way some competence interviews have gone. Your description of it as “institutionally racist” surprises me. Part of the thinking behind it is to provide a level playing field for candidates from disadvantaged backgrounds or whose circumstances meant that they don’t have the same job experience as other candidates. So to take a simple example, one candidate might have 4 A levels and a degree and have been employed for the past 10 years. Another candidate might be a parent who left school at 16 with no A levels, and who has only worked part-time because of family commitments. A third might be a new arrival from another country with no relevant UK qualifications and so on. But if they can do the job effectively, why should having A levels put one candidate ahead of another. So the focus is on the skills the candidate has, not qualifications or splendid work for charity (unless that uses those same skills of course). Having A level Greek or a degree in Computer Studies is very relevant if you will be required to use those skills in the job you are applying for, but for a shop manager or train driver and most other routine jobs they don’t prove anything.
I won’t ask whether you got the jobs you applied for because I am quite sure I know the answer but you might want to ask for feedback about your performance and have a think about whether you could have performed better. Many employers use this system and if you try to ignore it or fight it, you’ll find it hard to progress.