Of you are losing your weapon then you are losing your grip. If you lose your grip mid-swing then the weapon will have a lot of momentum and no immediate method of stopping it. If, for whatever reason, the weapon moves away from the strap, then the strap will pull taught and act as a hinge and the weapon will swing around it, eventually inverting its position and orientation relative to the strap. Typically, if one inverts the position and orientation of a weapon relative to the member that was wielding that weapon, it is a problem… A strap like that is all fine and good if you are sawing, or holding, or whatever else that doesn’t involve momentum, but once you start swinging, well, it is a good time to look into good-quality armours.
Not to mention, a weapon that is hanging from your arm is not useful in that state. You basically still need to pick up the weapon, it is just that you do not need to move to the weapon first… If you want to be immune to being disarmed, I would recommend getting a bandage and wrapping your hand closed and wrapping any wide points of the grip too. You hand will, of course, be completely useless for anything besides wielding the weapon, and if you are not careful you might cut off the circulation, and over time you might lose hand strength, and if you manage to lose the weapon anyway then you are not going to have much fun getting it back into the wrapped-up hand, but it would be much more secure. You get the bonus extra that it would make a strap like that actually useful because it would make the weapon far less likely to swing back at you.
I don’t know, I am working completely off of speculation here, but I just have this image in my mind of what happens if you have such a strap, hold it over your head, swing it down 90 degrees, release it, then immediately raise your hand over your head again. Yes, such behaviour would be deliberately stupid, but it demonstrates that risks exist.
