Im actually not a fan of using the lore to justify gameplay mechanics. There are an infinite number of things Spartans can do in the lore, that would never be included in a game.
But the sprint Mechanic itself doesn't make sense from a lore perspective. There's no reason that running really fast would prevent someone from pulling a trigger. You might argue that attempting to do so with accuracy would cause you to limit your speed... or it would negatively impact your accuracy. But there's no reason sprinting while shooting would ever be an impossibility for a Spartan or anyone else.
Also you can always right lore to explain a game mechanic. "During training simulations, Spartans are expected to have their gun ready to fire at all times". There's no need to do this, because games should be games first, but it's doable.
The question to be asked is whether or not having players move faster in one direction than all of the others is an improvement on design standards for arena shooters, and there are a plethora of reasons why it isnt- and actually makes the arena worse.
