This set up for Stamina makes traversing/looting a current location smoother.
However if the player is doing a lot of sprinting in their current location, they won't have much energy when they head out.
When well rested, it makes heading out to the next location with full sprint an easy task but by the time they arrive they are tired.
It restricts the player from running thru multiple locations.
Due to the multipliers when in motion and in place, the stamina recover time differs.
Increases/decreases as you jog and stop, looting and resting, ect.

This doesn't entirely throw away the current Stamina. (The short bursts of speed.)
A well rounded player with a full sprint bar will still use short bursts of speed to conserve their sprint bar for when they need it.
Reason being, over time if the player keeps sprinting everywhere around them and being very mobile, the bar will decrease & decrease. If they stay in motion it will take double the time to recover. If a player doesn't compensate for this and stop sprinting. It will further decline, eventually leaving them tired and forced to rest. Being penalized with only short burst of speed until they allow the bar to recover.

Give or take a minute off the total sprint time. Decrease/increase sprint running speed. Keep in mind multipliers on weight limits, injury, healthy-ness, and I think it'd be well balanced.