This is true in general, but the incremental benefit gets smaller and smaller as you get higher in the range. 1560-1600 are going to be nearly identical at almost any school. Above the 75th percentile, efforts to improve a score are usually better applied to other parts of an application - time is a limited commodity and prepping for SAT isn’t free.
Brown is the only school on the list where a higher score may be beneficial, but I’d still recommend investing time elsewhere.
(Unless there’s published data that I and Google can’t find, 1550 is the sum of Brown’s two SAT score 75th percentiles. The 75th percentile of the combined score is likely at least 10 points lower.)