There’s a point during which the bite wound is no longer able to be cleaned by using disinfectants, and MUST be treated with antibiotics. As I understand it, this is the time it takes for the contaminants present to spread from the wound site to your body as a whole - much like blood poisoning (entirely possible given the depth of wound). Tourniquets would theoretically work to slow infection if you were to say, apply a pair on either side of a deep bite wound before it hit the antibiotics-requiring stage. Constricting bloodflow would, like with venom, help to inhibit contaminants from spreading with it.
Unlike venom, disease multiplies, and may cause damage to the immediate area in ways the tourniquet still can’t account for. In real life, you also can’t realistically cut off bloodflow to an entire limb indefinitely. You’ll starve the whole thing and risk tissue death, and then gangrene. Applying tourniquets in real life involves something like 15 minute intervals (I have not researched actual values but it’s short-lived) of use and disuse, to reach some middleground of venom-stoppage without also suffocating the limb.
Tourniquets in-game could be balanced by letting them be applied for longer, lessening poison and potentially slowing bite wound progression, at the cost of slowly damaging the limb. At least, if you were going for that kind of an approach of pros/cons blending. Numb limbs slowing speed is also appropriate. Or maybe slower attack speeds for tourniquets on arms.
Logically, tourniquets can only be applied to limbs. The head, mouth, eyes and torso are unable to be treated in this way. Too impractical.