Good conversation, esp the part about trying to equate different loads/exercises relative to barbell.
When doing loaded pushups I'm pretty sure the load is, if anything going to = a heavier benchpress, but that's only because I can measure the amount of resistance my limbs are directly moving, and am supporting the load with my entire body.
Doing a single leg squat off of a crate with 105lb sandbag = nearly 300lbs the one leg is moving, but that isn't going to mean I could double the bodyweight component and make declarations about how I could do a 400lb squat for 15 reps. I'll say this though, it will definitely be more than double the sand - 210lbs on the bar, where 200lbs of sand would be virtually impossible for me to even shoulder let alone squat with two legs. 200lbs of steel shot I could probably manage just by virtue of its smaller size, tho it would still be far tougher than BB squatting the same weight with same approx body mechanics.
Having all the weight concentrated on a single, evenly balanced bar makes a huge diff in how the body can handle the load. Again, does this mean using those heavier loads will make for better strength in unrelated tasks? I have my doubts. MTI did a mini test using their Leg Blasters bodyweight complex vs BB Front squat, and both groups improved about the same % (keeping in mind the LB group wasn't training Front Squat). Again, small sample size, short duration etc but interesting nonetheless.
Still cannot argue the many good points already made and ones I've brought up as well - BB is the safest way to move big loads.