The SAT has 2 components with separate scores. The SAT score is usually the sum of both, but there's no reason colleges can't weight one section more than the other.
If you really care about multiple dimensions, add more types of standardized tests - general science (or specialized - separate physics, chem and bio sections), history, geography, whatever.
Or tell students to take the standardized tests that most closely map to their preferred major.
I still contend strongly that it is wrong to distill a person into a collection of numbers. They are not.
My mother was a special ed teacher who eventually became a diagnostician whose job it was to determine eligibility for services. Part of this job was to give a standardized test to a child to see if they met state set criteria. That said, this was only part of an assessment and was used along with parent preference, teacher recommendations, and other people involved with the process at the school. Outside of meeting state criteria, the numbers in the test were used to identify areas of strength and weakness to help understand a child and put this in perspective of a broader story. For example, if a child struggled with math, was it because they couldn't read well, struggled with the math itself, was distractable? There were also other instances where the test scores themselves were misleading. For example, did a child perform poorly because they were sick, or the AC of the building broke, or they set a test date on a school holiday when the child knew the other kids had a day off?
My point in telling this story is that the raw score in a standarized test can be helpful, but it does not tell a complete story. It is part of a broader assessment. The SAT and college admission is not different.
Purely using a test score does provide an objective score to rank a collection of applicants, but I still contend strongly that it misses the point. Depending on your point of view, college is meant to educate a populace, provide job training, give economic opportunity, or a whole host of other goals. One can use test scores a proxy to determine which applicants best approximate these goals, but I think we should consider whether they really help achieve this.
I'll also mention that using tests scores is not entirely "fair" either. I'd a friend who dated a guy who worked for Kaplan, one of the test prep companies. They had very good data about how much their test prep improved test scores. They were also very expensive. As a result, money and wealth can be used pretty directly to improve one's score. It's difficult for a university to fully address wealth inequality in society. However, since tests can be gamed so easily, I would caution against their over use.