I think it is important to have a diagnosis you have confidence in and that everyone who works with your child can be confident in. Getting therapies covered by insurance is important, but many psychiatrists also won't prescribe certain medications or therapies without a specific diagnosis. And, whether schools admit it or not, many times the diagnosis drives services, rather than the needs of the child. It shouldn't be that way, but that is the reality in many schools.
Our son was first diagnosis'd with Tourette Syndrome and ADHD, so we pursued medications appropriate for those diagnosis's (Strattera, clonidine). During this time, the school psychiatric insisted that difficult child had Asperger's Syndrome and difficult child got support from the school's autism inclusion program. We also pursued expensive therapy outside of school.
We made very little progress doing all of this. It wasn't until we got a bipolar diagnosis and started using medications appropriate for that diagnosis that we finally saw real improvement. We removed difficult child from the autism program and put him in a behavioral support classroom, which has been wonderful for him. Being in a class where the teacher and aides understand his diagnosis has made a huge difference in his outlook on school. And, using the right medications has made a big difference, as well. Honestly, I would not have allowed my child to take lithium without the bipolar diagnosis, even if a psychiatrist had been willing to rx it. But, it has been a wonderful medication for difficult child. Having a bipolar diagnosis put us in an entirely different universe and opened up options that we had not considered before.
With all that said, I am glad that we did not go immediately to a psychiatrist for a diagnosis. We certainly benefited from the neuropsychologist evaluation (and have done another since the BiPolar (BP) diagnosis) and we feel much more comfortable with the BiPolar (BP) diagnosis since we explored other diagnosis's and treatments first.