I realise that, and I don't expect, say, 101st Airborne to jump with two M1 mines per man (circa 10kg). Hawkins' at most (as they were issued one of those as far as I know), but I don't think it's far-fetched to say they would have received them alongside other support equipment dropped later. I do think it could balance out tanks a bit and any attempts at early light-vehicle rushing or "cheesing" around the flanks, and in general give infantry-heavy players a fighting chance against tanks.
Neither should it destroy a tank outright in one hit (unless we're talking light recon tanks), instead it would be immobilized for a time, buying you either time to get out of the way, or giving you an opening to use your AT-gun or hand-held Bazookas/Panzerfausts/Panzerschrecks/PIATs/what-have-you against a stationary, stunned target.