It's not linear because it's based on area rather than lines.

Or, to put it another way, the scale isn't based on square roots. It's based on the actual math that represents the physical properties of the system, and it happens that exposure doubles when aperture size opens by a factor of the square root of 2.

If you remember back to your elementary-school math, the area of a circle is πr². For a given aperture area A, how do we change r to get it to double? Well, we need to increase that r by a number which, when squared, is 2 — there's our √2.

We could certainly renumber those stops to give a linear scale, but since that would be an extra layer of abstraction from the physical system, that actually makes it more complicated rather than easier. This is more than theoretical, as the numbers are used in other places like flash guide numbers.

It's not really hard to understand and memorize the basic scale (since the practical range is only a handful of numbers anyway). In the 19th century, there were a number of competing systems using linear numbering, but by the beginning of the last century, the f-number system had won out.