Point is there is no synergy between sprint and high moving accuracy.
When it comes to sprint the only current issue is the "passive sprint" that is available to USF officers (and obers vet 5 if I remember correctly)
Why are you focusing so much on the action of sprint and not the opportunity it provides? The synergy is the ability to chase away the sniper or outright kill it by getting into position. Same as sprint into faust or Oorah into flame nade/at nade.
To give an example, a PF G43 player uses their 43 vision and/or flare to spot a sniper. A low level player will sprint into attack command, PF will attack at max range which means sniper will most likely retreat with some damage. However, a high level player will continue to sprint into mid-range and start firing while continuing to move forward towards the sniper allowing the player to take advantage of its high moving DPS.
Whereas a JLI player will sprint to about 25 range so and stay stationary to try and pull off one extra crit shot while sniper is retreating.
I am not saying sprint itself is a problem, PF having so much utility is the problem. They have a counter for a lot of different situations.