Basically you made the case for the metric system! Yes, sure, technically it's not that hard to convert between units, when all you're doing is focusing kn converting units. But in real life you're supposed to use your brain to do other stuff and if you have to stop and suddenly perform a contortion to compare the price per weigh unit of one item with another item that uses another base weigh unit, well, that's now an extra step that you didn't ask for.
With the metric system it can happen that some products use grams, and some kilograms (some countries use hectograms while others prefer decagrams, for some uses like food) and you have the same potential for inconsistency, however since there are only factors of ten at play, it doesn't take many brain cycles to quickly compare the numbers in your head.
I would say doing some forced arithmetic might do a little good.
My post is slight sarcasm but it's quite egregious to compare working out simple arithmetic to a contortion of the mind. Have more faith in humanity.
The inherent superiority of metric is small enough that people are going to be angry about this stuff, and yet it's dwarfed by inherent idiocy of inconsistent labelling which is solvable without a prolonged culture siege.
That said, traditional recipes tend not use ultra-precise units like '200ml'... Rather practical units like "a glass of wine".
I have a copy of an old famous French recipes book (French edition) and I don't think 'ml' is mentioned once and most quantities are explicitly qualified as being approximate.
Again, this is about being practical by using measurement unit readily available and acknowledging that everything will need to be adapted, anyway. This is a kitchen, not a lab!
A cup of chopped carrots does not seem odd to me. Again, it stems from practicality. You get a cup, you fill it with chopped carrots, that's how much carrots you need. Simple.
This is huge. In a way it doesn't matter whether the units are horsepower-seconds and farthings per cubic barleycorn or whatever, as long as they're consistent. But conversions are so much easier in metric that it ends up being a win for that alone. "recipe says 250g flour... I'll buy a 1kg bag" whereas the imperial equivalent requires you to know a long list of conversions between random units. As well as sometimes density, other times the "normal density" or something. That way you can buy a 1lb bag of flour to get 2 1/2 cups (or whatever, I have no idea how many cups of flour there are in a pound).
What enrages me about the American system is more the lack of consistency. Take something like mayonnaise. One brand will be sold with a price quoted in dollars per ounce, another in pounds, and yet another in x$/yoz for some y other than 1. And one will have calories per 2oz portion, one calories per 7oz portion, and the other calories per tablespoon (0.76oz) on the label. Obviously I made the numbers up, but this phenomenon is pure insanity. And it's blatant that the obfuscation is to enable exploitation of the consumer who has to perform arduous arithmetic to compare products. At least in the (pre-Brexit) UK the yoghurt had to have calories and price per 100g on the label, whether it was a 454g (vestiges of 1lb) pot, 500g, or some other size. I prefer consistency in some unit that I can learn to chaos.
As for recipes: why insist on measuring things of totally unknown density in cups? Mass is the appropriate way to measure strawberries or lettuce leaves, not volume.