Shipway,
You can disagree that personality doesn't play a huge part but try listening to what people who work at units are telling you. I know of people who were able to control but were chopped or failed because of bad attitude or a personality that didn't lend itself to teamwork. There are no wrong or right answers to each of those personality profiling questions because it is only the overall profile which builds a picture of you. Lots of people try to put down the 'right answer' unaware of how that will not work for them.
A recruitment manager once asked me if there was a queue at a two lane approach to a roundabout and I wanted to go left. Would I sit in the left lane and wait for the queue to move along, or nip down the right lane, doing one loop of the roundabout and then making the turn? You might think they 'want' to hear you would follow the rules, sit and wait and do things properly. But the people who pick the other option, breaking no rules whatsoever, generally have some component of what it takes to be an ATCO.
Comparisons with the police and military ATC are not much use as the police tests are very easy (yes, I have and did pass them and turned down a place with a force for NATS) and military ATC do a much different job. Only up to a 4 aircraft at a time in area but in very challenging and complex circumstances.