At a guess, when all screens had similar aspect ratio, a length measurement was more convenient: you can measure it without a calculator, and people can hold their fingers apart and think 'about this big'. We don't seem to have the same kind of intuition with area measurements.
I suspect widescreens have a bit of both. For watching videos or having two documents on screen, a widescreen does make more sense.
Sometimes I wonder if the proliferation of widescreens is due to actual demand, or just being more marketable.