Well, "well constructed" is the tricky part. It's not even clear to me what one would look like. K-12 schooling has a lot of goals, most of which don't involve literal transmission of information, but boil down to something like, "we want as many kids as possible to be normal members of society, with decent jobs, some sort of civic engagement, not engaging in criminal or shady behavior, and able to handle their affairs". Ideally we'd also like some subset to be brilliant, although it's not clear how much K-12 education influences that.

You can judge most of the goals in retrospect, say 20 years out: what proportion of kids ended up in jail, what proportion ended up with good jobs, what proportion are informed citizens capable of reading the news and participating intelligently in the political process, what proportion are able to handle their personal finances, nutrition, health-care, etc. successfully, what proportion won prestigious awards or started successful businesses, and so on. But writing a test for 18-year-olds to take that predicts all that accurately is pretty hard, and as far as I know, no tests have shown even plausible evidence of their predictive power in that respect, especially when you control for demographics.