Without testing there is no learning or teaching.
And if it cannot be tested, then nothing was learned or taught. If you know someone learned it, it's because you tested them somehow.
The tests themselves should be tested, or all the test items should be scrutinized to ensure that they perform their (culturally neutral) function of objectively measuring each student's mastery of the subject matter.
the problem is that this is impossible - the only thing a test can ever measure is your mastery of taking the test, but it's almost completely unrelated to mastery of the subject that the test is about.
No, mastery of the test is about the same as mastery of the subject matter. Knowing how to answer the test questions is the same as knowing the subject matter. There's no difference between knowing something and knowing how to answer questions about it. You can't claim to know something if you can't answer questions about it. The better you know it, the better you can answer questions about it.
You can't give an example of someone doing well on the tests but not knowing the subject matter, unless it's a bad test which could be made better. Also you can't give an example of knowing the subject matter but not being able to answer questions about it. To have learned it, one must have more than only a degree or an accumulation of classroom hours. Whereas ability to answer questions about it is demonstration of one's knowledge of the subject.
the problem is that people are stupid enough to think that one's ability to master a test is the same thing as one's ability to master the thing the test is about, . . .
They are the same, as long as the test items are really about the subject matter and not something artificial or superficial to the subject matter. The tests can be improved so as to focus better on the intended subject matter, so they can perform better at measuring the student's knowledge. So the flaws of the test can be reduced, and we can rate the test, or test the test itself, to improve it.
. . . and that has led to a huge number of problems in US culture when it comes to notions of intelligence and career preparedness.
What "problems"? You can't name them without tests you're using in order to make that judgment.
If you really believe those problems exist and want to correct them, then you want to improve the tests to make them perform better at measuring the knowledge of the students. But without improving the tests, you are proliferating the problems caused by bad tests. Also increasing the good tests helps correct those problems. You have no way to correct those problems without more and better tests.
the population needs to understand that testing only tests one's ability to test, and if that's the data point we're going to use to judge people fine, but stop pretending like taking a test is analogous to understanding the material.
But
"understanding" the subject matter is the same as doing well on tests, or being able to, or able to answer questions about it, or to perform what the subject matter is about. The phrase "understanding the material" is meaningless if it doesn't mean being able to perform well on a test of one's knowledge of the subject matter.
You can't give an example of "mastery of the subject" or "understanding" it or "ability to master" it which is separate from one's ability to answer questions about it or perform well on the test about it.
If you dismiss the testing as unimportant, then you also dismiss the subject matter as unimportant. You can't claim the subject matter is important, or any learning of it, or teaching it, if the testing of it is not important. If there's nothing there needing to be tested, then there's no subject matter needing to be learned, and nothing to be educated about, also no "problems in US culture" needing to be fixed.
Either we improve the tests, and test everything that matters, or -- nothing matters and nothing needs to be learned and no "problems" exist and no "education" is needed.
To say tests don't matter is to say truth and knowledge doesn't matter and that nothing is worth learning because nothing matters.