twhy do these other federations insist on Monolift / wraps, and squatting the bare minimum amount of depth (from the videos I've seen, mainly PTC)?
Same reason they don't all test for drugs, or they have single lift meets. Because they want to lift more weight.
Wouldn't it be in everyone's best interests (and less drama / argument over records or judging) to have everyone across feds doing the same movements in the same way?
But then they would lift less weight. And it'd be much harder to get people in the "top 10 squats of all time", etc.
If you can say, "we had a guy total 10 times his bodyweight" or "we had a guy total over 1,000kg" or "we had a guy squat 1,000lbs", this brings you glory and fame. The vast majority of people won't know the difference, they'll just see someone with a fucking humungous weight on their back or in their hands. The people who know the difference either don't care because they use a lot of that stuff too, or else they don't use it and don't think much of it, but these people are not the targets of the marketing - it's the wider public who don't know the difference.
Long-term it'd be better to toss aside all that stuff and just lift. Short-term you lift bigger numbers. Long-term you get illnesses and injuries (from drugs and equipped lifting) and alienate the general public and potential lifters from the sport (since, as in IPF's equipped-only days, people go "WTF is all this shit?") But short-term you get to put up bigger numbers.
People tend to focus on the short-term. Human nature.
Nonetheless, Kristos is strong as fuck, and did not need dodgy judging to get three white lights.