They just want public education to do a better job. Here's the corporate do-gooder method. Even their advocates acknowledge that the tests are imperfect. In some states they're administered even before the new curriculum is institutionalized, so kids are tested on material they never learned. The tests are poorly designed political compromises.
Tests are simply more cost-effective than fully funding schools.
Cynics, mostly liberal ones, reject much of the standardized testing agenda as merely a conservative ploy. Standardization's real goal, they argue, is not to improve public education but to destroy it. Since only public school students take the standardized tests, kids whose parents can afford private schools don't have to agonize year after year about potential failure. All those people making money off parental panic makes cynicism pretty understandable. Still, conspiratorial types have yet a different analysis.