On the testing, I can certainly understand your points and the inaccurate test results. IME, people newer to the hobby are not using RO water and are not rolling their own fertilizers. Unknown tap water and a capful of whatever magic aquarium plant juice the pet store sold them is what they got.
Testing can give us some idea of what's going on. Of course, if the test kits are not expired and they did the test correctly.
If ICP testing were cheaper and easier to do, would you feel tempted to test a few times a year to see if your math matched?
I am much more likely to test tap water than tank water, quite frankly. While people on on FB and this forum might be using RO/DI water. That is not what most people use when I speak to hobbyists at club meetings. And if they don't know what they are putting into their tanks, they are going to be fighting an uphill battle from day one. There are ways of managing things if they know what's the tap water, even if it limits plant selection.
As far as ammonia and nitrite are concerned? IMO, the best medicine for that is patience. Something sorely lacking in the hobby among beginners. If I could bottle THAT, there would be no need for ammonia or nitrite kits. (for the most part... I know there are exceptions)
I hate API, not only because the test kits are hard to use accurately (though Bailin Shaw tells me if they are fresh, and shaken HARD and LONG enough, they are accurate... but how many newbies know to do that?) But also the "Master" kit is not "master" enough to be suitable to trouble shoot even a low tech planted tank.
I rarely test tanks, but when traveling in the wild, Christel and I have always liked to double-check (or triple check) our results. I usually buy a new, complete, Sera kit before a trip, and she has a new German kit... can't remember the brand off hand. Our test results have always shed nicely, AND have been fairly close to the lab results on water samples that she has taken back home to be done in Germany. So I feel quite confident in the Sera kits for my purposes.