I thought having the dmi at the start would be the best idea.
You go through the whole process and they're spending money on you taking the tests and then you have a dmi and fail it because you're not suitable for them that's just a waste of every bodies time.
It works both ways really. I'd say the current way is best, because you could be interviewing 200 applicants, of which 100 don't meet the criteria the other tests test you on. At least having an interview last means you have demonstrated you meet the 'tried and tested' basic skills to proceed on to a course.
I know different agencies work like you suggested would be best and it strikes me as strange to be honest. For example the Fire & Rescue Service (Hants specifically for retained staff) basically employ you after an informal talk with a station manager, a few weeks later assess you on your physical fitness and your mental aptitude, then give you a formal interview. The medical is thrown in somewhere in the middle at HR's usual pace.
All well and good, but why have somebody on the payroll who may not be cut out for the role? In fairness, you have a few shots at the tests, but from a business point of view, would it not be better to asses potential new recruits first, before spending further money?