But I'm just curious, with formulas like this in mind, how does the REST of the world calculate things like Total Gravity, Pounds of Grist needed, etc. Like would they just use °Plato instead or do they have entirely different formulas?
The formula is actually the same, it's just the constants and units that change. So instead of representing potential extract as, say, point-gallons per pound, you'd use degree Plato-liters per kilogram, and so on. Base malts tend to be around 37 point-gal/lb, which is about 77 °P-L/kg. If you want to brew 20 L of a 12°P (1.048) beer at 80% efficiency:
(20 L * 12°P)/(77°P-L/kg * 80%) = 3.9 kg
or in American customary units: (5.25 gal * 48 points)/(37 point-gal/lb * 80%) = 8.5 lb
The two answers are the same, just given in different units.
°Plato tends to be more common in Europe, SG in the UK, and American brewers use whichever they learned first, more or less.
The imperial system makes so little sense to me, I do all my measurements in metric. I couldn't tell you how many ounces are in 3 pints if my life depended on it.
The real problem with the "imperial system" is that unless you specify which "pint" and which "ounce" you're talking about, you can't even come up with an answer.