First and foremost, it changes map design. Maps have to be larger, structures have to be longer, it completely changes the way the game is played. Play a faithful recreation of The Pit or Guardian or Midship with Sprint, you'll notice it right away.
Then, it takes away from gunplay. What were once key battles, are just games of cat and mouse or hide and seek. Instead of having a gun duel, the weaker player will just run away and force you to come after him. Or you won't come close either. For example, on Valhalla, I've clearly outduelled someone, and right before the killing blow, he decides to run away and hide. Now a lot of people did that without sprint, but with sprint, it's a guaranteed get out of jail free card. Player movement is slower, so that I have little hope of catching up to a guy sprinting. He out runs shots, grenades etc.
All the reasons you listed are vital too. I don't know, I'll try to go into more detail later. If you want to make the game faster, increase movement speed, increase strafe speed.