Another thing affecting a lot our pure math is the arching of the bridge: of course low first (and fourth? ) need to be bigger than high third and second.
So, scaling tension is required
Plucked or bowed instrument: the big string offers more friction under the bow so someone may think a smaller string would react better. This is the idea driving modern strings.
I have to add that I experienced the opposite: a more tensed string allows me more colors and gives more support under the bow.
Fingertips, or feeling: this may be deceptive.
A small and hardened string seems stiffer under our finger, so we would like to have it less tensed.
But, less tensed means smaller, so it would hurt the finger more. So maybe we would like it bigger and softer? Uhm....