But you can also give problems, like 'here are the dimensions of some real-world problem, and here's a formula used to solve such problems, apply one to the other'; or 'here's the text of a poem by so-and-so, explain what you think the poet means and support your arguments with reference to the text.'
I know essay answers take longer to evaluate and are harder to score, but I get the impression that way too much of k-12 educational testing involves multiple-choice questionnaires.
This line of thinking is IMHO a lot of what's wrong with modern education: none of that stuff matters if you don't understand what's behind it (how you get to the formula of calculating the hypothenuse and why people fought WW2). To use the WW2 example, the answer to "who" is "Germany&allies vs Russia&allies" (an oversimplification), but it's far more important to know why they were fighting (a fight between different political ideologies, including Nazism and Communism). Education focuses too much on (possibly useless) facts, and far too little on the logic behind them, or why they matter.
BTW, you can't get a license to practice medicine without passing a standardized test.
I can't help but feel that the problem lies in a fatal combination of non-filtering teacher training (as sentimented by "oh, anyone can teach", and as mentioned by that recent Finnish education post), community culture that talks more than acts about the importance of high quality education and self-motivation, and a lack of funding for those (like OP) who give it their all.
edit: I also think that we should encourage a sense of trusting (maybe government-trained) educators with being able to identify which children in their class need to learn what, better than a test could. I'm not so sure what the benefit is to ignoring the individuals at the 'dx' scale of the educational calculus.
By which I mean, when kids can't memorize all the stuff that they have learned by heart, and then when they can't produce an exact replica of a procedure or something without some kind of reference, we equate it to their not having learned it in the first place.
Programmers create docs for the purpose of referring to them, doctors must look things up as opposed to simply relying upon a faulty memory, etc.
Kids get the impression that to learn is to fill their memories as opposed to be able to analyze in new scenarios, and that if they can't memorize facts then they are a 'bad learner'. These standards just aren't fair.