MOVEMENT SPEED

I don't think its the base speed at all. If you just run in a strait line i feels very average, which for a character carrying gear would be as expected, not sprinter speed but your getting shot so a bit of hustle.

I think the issue is the direction, and elevation change speed, especially from a sprint.

I would like to see penalties for movement speed if you spam inputs or coming out of a sprint (strafing back and forth, spam vertical peaking, diving into a room to shoot)

I think if they keep it realistic, they'll nail it. A solider can probably get moving pretty quick running for his life through a war zone the strait sprint speed can stay high, keeps the movement though the map and back into action short. Hell let loose and games of that speed are bad for this cause if you have a bad game you spend an hour running back to the front to get killed and start again. 

However, No one is able to swan dive, land chest and or face first into a metal gun, shoulder the rifle and start firing accurately in sub 1.5 - 2 second times. Or knee slide though a door while ADS and shooting accurately. Those base movements i think are good to stay because it is movement that is realistic and could be useful in many ways, but needs heavy time penalties so if you use them offensively you have to be perfect, know were you target is, move cover to cover still but can use some high profile movements to do it. But you can still use them defensively to take cover quick and not abuse it to attack people while flying though that air or something.

I think they would fix a lot of the feel without making it blatantly slower like a slider would do by adding delay, or like a bigger slow down effect after sprinting. That way running would suck in combat so people would choose to walk and keep their weapon up slowing down the gunplay, but the rest of the game, running around, getting vehicles, running though unpopulated areas of map wouldn't be painfully slow.