OP is getting power and force mixed up. Power is work done (force times distance) in a unit time.
So increasing your max squat increases force. It may or may not increase your power.
Lots of exercise bio studies on force x speed of contraction. As speed of contraction increases, the force of contraction decreases.
Think about a slow squat. You can do your max squat over a slow squat. If you want to speed your squat up, you need to decrease the weight (maximum force decreases).
If you do this over a number of data points, you can find the power generated at each speed. If you graph it with power on the Y axis and speed in the X axis, you will have a curve that is at its highesf somewhere in the middle.
The goal of sprint training is to push that peak as far up and to the right as you can. Here is an example of a page explaining it a bit more:
https://courses.lumenlearning.com/boundless-ap/chapter/control-of-muscle-tension/
To directly address the OP's question, simply training to increase max squat (or other max lifts) while maintaining body weight isnt ideal sprint training, because you also need to train for speed.