I don't think 1.77 would make more intuitive sense to the average consumer of this type of product than 16:9, for the same reason that you don't typically write

I don't think 1.77 would make more intuitive sense to the average consumer of this type of product than 16:9, for the same reason that you don't typically write "add one unit of flour and 1.33 units of sugar" in a recipe. Particularly for screens, which most people think of in terms of two dimensional surfaces, using simple fractions seems more obvious, and for ratios like 4:3 and 16:9, numbers are particularly useless because they can't be used to exactly describe the relationship.