I like that, giving faster sprint a stamina bar to have it balanced.
We already have a faster sprint, which you can do by running with a knife/repair tool/defibs out. The downside of this is that you don't have your weapon available, so if you get caught in the open, it would get you killed.
A stamina bar works wonders for games like Dark Souls, where the entire combat is balanced towards you having to maintain your stamina. The combat is predictable, follows a reasonably steady flow and the difficulty comes from learning the movements of the boss and learning how to respond accordingly while still managing your stamina.
The stamina bar has one critical downside though. It doesn't work for games where the combat flow is unpredictable. If you can't predict when you'll need it, you'll either underutilize it, or you'll use it at the wrong moments. This leads you to the stamina bar being unavailable when you most need it. That's why many games including Battlefield shifted away from using stamina bars to manage sprinting speed.
In addition to that, it just creates downtime. If you feel like you'd need the stamina bar, but it's still busy recharging, you're just waiting while doing nothing. It breaks the pacing of the game.
