Geoffers, I have to agree with your assessment. As a check and training pilot in both the VFR and IFR worlds and crossing a few continents I have also witnessed, to my dismay, the disparity of skills and knowledge you are talking about. I personally believe that in addition to competency based training there needs to be a move toward competency based employment but that is a topic for another discussion.
I have to say that the instructional world you are describing is very much what Helilog56 tried to describe earlier: what we have had in Canada. There are some attempts lately to dumb it down by both industry and individuals but the essence of the system remains: 4 tiers of instructional licencing, required mentoring/supervision, legislated recency and recheck, and (importantly) a minimum experience level for receipt of the rating.
This system isn't perfect but it very closely mirrors the military system that Crab has described. Because of an accident that put a serious hiccup in my career many years ago, I have passed through both certification processes. The biggest difference was the quality of the instructional courses: the military was far superior to any civil instructional course I have received since.
The key ingredient to this system is an entry barrier of 400 hours PIC to obtaining an instructional rating. As all of you cry out in dismay remember that a very large helicopter industry does very well relying on this system. Yes, training in Canada costs more. There are fewer places to train. They also pay better because they compete with commercial operators for staff. Better pay means it is more attractive for experienced pilots to consider instructing in their off season whether that be weekends, winter, or the back side of an equal rotation. There are also very skilled pilots whose career is flight instruction. The higher pay means it is a viable way to feed the kids.
Commercial operators then are forced to get low time pilots from a licence to employability without relying on the feeder system that other nations use and these guys and gals must prove their work ethic to get through the process.
Flaws and abuses in the system? Of course. As has been said here, any system will be abused by the individuals who have that proclivity. Do weak pilots carry on? Yes, but not nearly at the rate I have seen elsewhere.
Back to the original question of how to choose TRI/TRE candidates. I believe that it should be the Chief Pilots and existing Trainers who identify the line pilots with good skills and knowledge. These are then encouraged to learn more instructional skills by steady progression through LTC, TRI, SFI, TRE, etc. The individual who just really wants the extra pay and is beating down the door is just as likely to be the wrong candidate. Yes, seen that many times. Pay close attention to the one who has the respect of his colleagues but does not covet the 'title' of Training Pilot.