They are one of the most background-blind ways of establishing student intelligence and creativity, as they have been shown in studies to measure the ephemeral 'g' value representing general intelligence very well.
Now, critics say that impoverished students do worse on the SAT than students from wealthy families, but the fact is that study resources for the SAT exist for free on the internet as well as for low cost in the form of study manuals. Poor students from certain communities probably don't have the same encouragement to study for the SAT as other groups, especially wealthy families. Fortunately, cultivating a culture which encourages study for standardized tests in theory costs nothing.
This puts poor students on a much more level playing field than if we base elite college admissions on things like high school quality, which is already a huge determinant of admissions at top colleges. Unfortunately students can't use free online resources to get into top private high schools. Doing so requires their parents to be well off enough to afford the high cost.
Judging students based on grades is also very difficult because of grade inflation, which obscures things.
We will never be able to fully eliminate the influence of wealth on college admissions, but standardized tests offer the best conceivable way to fairly judge students of all backgrounds.