Also, SI units makes perfect sense if you have grown up in a country that uses them exclusively.
Well sure - if you grew up with no alternative, you will of course think it makes sense: because you are taught to think in the system and don't get to understand different ways of doing stuff. It's like English people find the gendering of inanimate objects like tables bizarre as there's not really grammatical gender beyond people/animals, but the French happily do it as that's what their language does.
With units, I'm pretty 'bi-lingual' and can understand both sides - some things I prefer customary (estimations, body weight/height), others metric (science stuff), others I'm indifferent (distances, speeds - though km/h rather the SI m/s). There's good and bad features of both systems, but most of the time they are just different, rather than better/worse.
And it is a system of units that works together making it very easy to do calculations in your head. To quote Josh Bazell:
Bazell's quote (in green) is a bunch of nonsense. First off, it's far from pure SI and so needs correcting:
"In metric, one milliliter 1cm^3 of water occupies one cubic centimeter 1000 mm^3, weighs one gram, and requires one calorie 4.184J of energy to heat up by one degree centigrade Kelvin —which is 1 percent of the difference between its freezing point and its boiling point."
Using the metric-based customary units like litres and calories is cheating - especially if talking about SI, which is even more specific. Metric in general, and especially the SI system that's a subset, doesn't like these special units and seeks to get rid of them, whereas the customary system embraces such alternative units (of volume and energy in this case) if they are useful. Do you know your 4.198 times table off by heart to do it in your head? A level chemistry we were allowed calculators just for dealing with stuff like that (and we used the rounded 4.2). So often customary has digs like "do you know how many fathoms in a furlong?" even though you'd never be ploughing or horse racing downwards through the sea and so don't need to know it's 110, but you never get "do you know how many Joules in a calorie?".
And lets not forget that centimetres are only really tolerated as they are the foundational, original, metric unit (defined before the metre) - it would be 10mm or 0.01m if it was pretty much other unit: we never talk about centi-Amps, or hecto-Joules, and prefixes are only really multiples of 10^3 other than for units of distance, area and volume (ie metre-based). Hence why I converted to cubic millimetres.
As for 1% of the difference between water freezing and boiling, it's totally and utterly useless as a concept. Celsius has a nice zero point - but the percentage thing is just arbitrary - even assuming base-10, why is 100 important? Why not 1000 as the SI prefixes go: kilo-, mega-, giga- (1000-based) rather than hecto-, myria-, mega- (100-based). Likewise if 100 was genuinely special, we'd be using grads (400 to a circle, 100 to a quarter), not degrees (360 / 90) - of course, there's 180 degrees Fahrenheit between water freezing and boiling: same as half a circle. That Celsius is a centigrade system is only cool-sounding because we decided it was cool-sounding - objectively it isn't.
Personally I find the way that Fahrenheit set up his 96-grade scale more mathematically cool with its repeated halving, and water freezing a third of the way between the two bounds - but both are completely meaningless scales in and of themselves - its experience that tells us actually how big a degree C or F is, not the concepts behind how big a degree is. It's the anchor points that have meaning, and Mr Fahrenheit went with the wrong anchor points (though water freezing is a third anchor a third of the way up and if it was where zero was put, it would be less weird and the UK would still be using that scale).
"An amount of hydrogen weighing the same amount has exactly one mole of atoms in it."
OMG there's 60,221,407,600,000,000,000,000 atoms of hydrogen in a gram! What a totally unmeaningful thing!
Moles are just a fancy way of getting stuff in the right proportions* - there's zero reason why there couldn't also be a number of atoms that leads to a customary weight unit (pick whatever one you want), or a gallon of gas, or both. As long as you are using the same multiplier in your calculations, it doesn't matter. Likewise there's no reason why there couldn't be a pseudo-metric unit that's the number of atoms in a litre of gas (to remove the 24 - or 22.4 now that stp has been changed from 20°C to 0°C) - other than having task-specific units to make the numbers nice is antithetical to the metric system - as we see below when I have to throw in the specific heat capacity of water for the metric calculation, but not the customary.
*proportions, of course, being easier if you aren't obsessed with 10 and percentages. Defaulting to thinking in percentages was, IME, the biggest barrier for my peers during our education when engaging with fractions. Those who thought in fractions by default could still deal with percentages just as well.
"Whereas in the American system, the answer to ‘How much energy does it take to boil a room-temperature gallon of water?’ is ‘Go **** yourself,’"
This is a different question! If you are going to have to move the goalposts...
Taking the original question of heating 1 degree, it takes 8.34 BTus to heat a (US) gallon of water 1F - it didn't take me long to work it out - I just had to work out pounds per (US) gallon and it's 8.34 - this takes no time at all nowadays with Google. A British Thermal Unit is 1lb of water 1F - customary can also do the same stuff metric is being praised for by Bazell - only metric actually doesn't want to do that stuff and, at-best, merely tolerates you using calories! Air conditioning in America uses stuff like 'ton of cooling' (freezing a ton of water in a day = 12000BTu/h) and BTu happily - units like these that are task-oriented and make the numbers nice is a feature of customary, not metric. If they wanted to do it by volume of water they could use units that would do that - but they measure water by weight not volume there, just as they measure flour by volume (cups) rather than by weight when baking...
And let's look at "how much energy does it take to boil a room-temperature [mass] of water to boiling". First off, we need to define 'room temperature' - we'll go with the formerly-standard temperature of 20°C / 68°F. We'll also assume the formerly-standard pressure of 1atm (since changed to be 100kPa, because the 101.325kPa previously used was too real-world and not artificially round enough!) so that water boils at exactly 100°C /212°F. A kilogram of water takes 80kcal to heat from room temperature to boiling, but that's metric-customary, not SI, and so we need to get the calculator out to multiply by the specific heat capacity of water (4.184) to arrive at the answer of 334.72kJ. A pound of water takes 144BTu to heat to boiling (a gallon 1200.96BTu, for completeness). Which is easier? Customary as it fudges out the constants! Though, sure, the metric-customary is a little bit easier than the US-customary as 100-20 is easier than 212-68.
"because you can’t directly relate any of those quantities."
But customary can do that, and in better ways because they don't try and insist on a single one-size-fits-only-one-thing-if-that unit per thing being measured and so can smudge out constants. The problem is that it's in the hands of Americans who like saying saying what they see ("sidewalk" etc) and so units done this way get called stuff like 'foot-acre' or 'foot-pound' rather than some fancy name from Latin or after a scientist that makes it sound like some magical convenience that they line up rather than simply a definition of the unit.
How much weight does a mass of a pound have on earth? A pound (OK, that a pound-mass and a pound-force are both a pound is confusing, but the numbers are directly related). How much weight does a mass of 1kg have on earth? 9.81N - there's a constant getting in the way!
And of course, 'directly relate' is a funny term to use with metric - given that it deliberately tries to not be directly relatable to reality. Take that original foundation unit - the centimetre: a billionth of the distance between the North Pole and the equator via Paris. An unimaginable distance (that took them years to calculate, and even then it was slightly off because it was a deliberately obtuse constant to work off) divided by a unimaginably large number. We only know how big a metre is, because we learnt how big a metre is - at least with a foot we could get a intuitive estimate from the definition!