A pick-up will pick up (!) the sound a string is making just above it. The three pups on Strats are (or used to be, originally) identical. The string vibrates at a different amplitude - hope it's the correct word - as in the movement is greater the closer to the string centre you get. So by the bridge, the pup will hear a tighter, thinner sound. One uses the pup configuration one likes for a particular situation. Generally, neck pups will give a rounder sound, more suited to chord/rhythm playing. Les Pauls have a 'treble/rhythm' switch, between bridge and neck pups.
I guess Leo thought that if you wanted a more piercing sound, thus using the bridge pup, there would be no necessity to attenuate the sound with a tone control. Jazz players will often use the neck pup, and roll some treble off that.
It emulates where you pluck the strings, to a degree. As in, if you use a pick close to the bridge, then the sound will be a lot less bassy than anywhere else. That's the sort of tone that the bridge pup hears.
A lot of guitars these days will wear different pups in different places along the strings, and can be switched in and out of phase.
The middle pup gives a sound somewhat between the other two. Fender was an electrician rather than a guitarist, but realised that there was another sound to be harvested between bridge and neck, and on the original guitars, he only had a 3-way switch. We soon found that it could be put carefully into the 'in-between' positions, giving 5 options. Later, Strats were equipped with the now common 5-way.
This still left a decent sound unavailable, that of bridge and neck combined. A Strat I played some years ago got over this by having 3 push button switches, one for each pup. This gave 2 more options also - all on and all off ! The bridge and neck combination on my own guitar ( not a Strat) is one that works well for rhythm playing in a big band situation - the roundness is there with an edge to cut through for the more choppy bits.
I played a bass last year, Steinberg, maybe, that had one pup, that was slideable on rails. The tone could be changed by moving it about 4/5 " between bridge and neck. Different !