Lots and lots of great points above. I especially like polarbear's rephrasing of the question - "what are my child's educational needs and what do I need to do to get those needs met".
We tested the first time when DS was 6.5 because school was a disaster. He was struggling with writing, frustrated that everyone else was writing without effort and at the same time frustrated that other things were too easy and repetitive. He takes a LONG time to warm up to people and wasn't very cooperative with testing but both he and the tester did the best they could at the time and the resulting 14 pages of report and an official label of gifted/probable LD helped us improve the school situation (it wasn't perfect but it was at least improving). We tested privately - WISC, WIAT, Connors and a few other things.
We retested (WISC, WIAT and I can't remember what else) at 8.75 and he tested much higher and got an official LD label. We again tested private with the same tester and he was a lot more comfortable this time around so I think that helped.
I will say that finding a good tester was key to our situation. She was very, very good with him both times we tested. Usually watching other adults try to deal with him when he's stressed out is painful (doctors, dentists, optometrists, coaches, teachers, etc...) but she figured out in 2 minutes what DH and I have slowly figured out living with him 24/7.
In between all of that the school tested him with the Canadian version of the Cogat which was high but nothing compared to his WISC scores.
So I guess our experience was the opposite of eco's regression to the mean. Nothing that the school did in grades 1-3 would have helped raise his scores in anyway - they were too busy focusing on the LD and behaviour. He's now moved to a congregated gifted class and that has been life changing for him. His comfort level could explain it or maybe there is a bit of asynchronous development that factors in as well. DS was speech delayed (enough to qualify for free government therapy until age 3 when he "graduated") so he definitely has never followed the typical curve.
Having spent many thousands of dollars testing privately I will say that having the school do something other than Cogat would be pretty amazing. Then again if the tester doesn't have experience with 2e and you can't retest for a couple years that might make paying privately worth it in the end (not sure if that is part of your debate or not but figured I'd mention it).
