I always thought of it as a in an emergency it's better than nothing and can be found in many homes and in many women's purses.
Nope.
In a penetrating deep bleed, you need to stop the blood leaving the blood vessel, not the body. This is why, on extremities, TQ's are highly recommended. In a joint area, or somewhere you can't get a TQ, you switch to wound packing (rolled or Z-gauze). The idea there is you jam your finger down in the wound, find the severed blood vessel, and pack gauze tightly right on the vessel, creating an internal pressure dressing, that molds to the wound channel, and slows blood loss enough for a clot to form on the vessel.
A tampon, being a compressed cylinder that expands circumferentially, does not put pressure on the blood vessel that is leaking, but rather on the sides of the wound channel. This doesn't stop the bleed, just converts it to an internal bleed. It may make you
think you stopped the bleed, but home boy is still bleeding out.
If you have a bleed that requires packing, and you don't have gauze, you are better off either attempting to hold pressure on the artery upstream or sticking your fingers in there and holding that MFer closed till EMS gets there.