Acceleration should still be a factor when the sprint button is used. I'm not sure the game does that part well.
But in real life terms, if I am not trying to run full speed, I should never get to full speed, I should max out at maybe 3/4 speed. And, if I am starting from 0, how soon I get to 3/4 speed should depend on my effort. That is why the sprint button should be there.