1) They test ability to synthesize information and marshall evidence in support of a clearly articulated argument, rather than rote memorization and the ability to regurgitate facts under time pressure.
2) They test students on real-world skills (which includes knowing where and how to look up information and what to do with it once you have it) rather than mere test-taking ability, which helps mitigate the fact that some students are simply poor test-takers.
3) They elevate the quality of the work, which makes grading easier and fairer (its difficult to fairly assess a student whose handwriting is so poor that you cannot understand what they have written).