Scholastic Aptitude. That's what the test is measuring, your scholastic aptitude, and in most colleges the style of teaching/learning is lecture/notes/testing, at least at the lower levels. It's the methods of a "scholar" in the traditional sense. That's unfortunate, but it is what it is. The test is one measurement tool for colleges to guage how well you will probably do in that traditional scholastic atmosphere. They have to have some objective tool to weed out those who will probably not do well, so they can maximize their dollars and their limited space/resources. It's not the only tool, though. There is the essay and the portfolio of activities and achievements throughout high school and post high school life. Life experiences count for a lot to those who have been out of high school for a few years and are going back to college. And that's all in the typical college application.
I personally know a student who had very high grades in a very rigorous high school program, who got high SAT scores, and who was not accepted into a state university, and the only reason he could think of was that he admittedly blew off the essay and made a joke out of it. Probably because he thought that with scores like his, why should he have to write one. That said as much for a low aptitiude as his scores might have said about a high aptitude. The college decided that with an attitude like his, he didn't have the aptitude to do well in the university setting.
Why the stress? Because there's also a lot of MONEY riding on high SAT scores. They can lead to scholarships, lots of scholarships.
Should there be other ways? Probably, but can you think of a way that is as objective and cost effective as the current system of SAT's, essays, and college applications packets? I can't.