As far as US use of bayonets: they are weapons, and therefore are kept in the armory where they are issued along with rifles, machine guns, mortars, etc as needed. The self-injury and theft rationale is false. Most troops have far better knives of their own with which they can stab themselves and each other. If you can't trust your warriors with bayonets, how the hell can you trust them with rifles and machine guns? The USMC has always trained in the use of the bayonet, so if this is against the "rules", somebody better let us know so we don't get in trouble. Also, I would take Col. Grossmans comments with a very large grain of salt.
I'm not familiar with IDF policy on bayonets. I was thinking that if it is true that they do not issue them, it may be because of PR reasons, but they have never seemed to be overly concerned with political correctness.