I think test kits are an essential part of the treatment system. Having said that, it depends on the test kit. The standard methods of examination for water and waste water lay out the acceptable techniques and systems for water testing. They are not mandatory and a domestic supplied test kit most certainly wouldn't have to follow the methods laid out or use the reagents specified. Therefore testing in some cases could be hit and miss.
However there also needs to be perspective. An aquarium is an artificial environment and maintained by artificial means. Therefore a test kit may be the only viable source for some information.
The volumes of aquariums are considerably less than a natural water bodies volume would be in most circumstances, so again consideration must be allowed for this.
Testing of itself is only an indicator. And as indicator is indispensable. However as with any other indicator the results require interpretation. It is unlikely without extensive experience and exposure to lots and lots of water tests, good and accurate colour vision, training in how to correctly use a test kit (particularly colour metric based comparators) consistent and accurate results would always be obtained. For this reason it is likely some people would be disinclined to entrust their tanks to test kits.
On the other some individuals would have persevered over time and accumulated sufficient experience through trial and error to obtain reliable results for the purpose.
Like many things in water treatment unfortunately, confusingly, everyone is right.