Cups are not weird, just just a pain in the arse because US cups are 240ml and metric cups are 250ml. If you're following a recipe that needs exact measurements it often trips you up.
Yes they are. For example, the article talks about "dark leafy greens (about 5 grams per cup)". Is that cups of dark leafy greens before chopping them up or after? If you specified the amout per weight, it would not make a difference. If you specify them by volume, it does.
More generally, and anecdotally, I had a health scare that resulted in going through a fairly standardized regimen including exercise and dietary advice. I received many pamphlets and handouts! There seems to be a substantial effort to convey health advice in a way that downplays or minimizes any kind of math. People just freeze up when they see math.
This could give rise to an effort, from a public health perspective, to come up with units of measure that people can use without being put off by math.
For the non-US-non-cooks: 1 cup = 240 ml ≈ 1/2 US pint
Using volume for those, the amount you’re actually using can vary by a factor of 10 depending on how granular it is, how finely chopped or shredded it is, or how it fell that day.
I do everything in grams, but with some recipes and labels it’s just not possible to know how much of something it’s talking about. Which is unfortunate because that’s the entire purpose of a recipe or a label.
Why can’t we stop this?
Well, the recipe should give you an indication of granularity, although you won't get an ASTM number. That said, for cooking you're supposed to eyeball it a bit and judge through experience. Rarely does a little too much broccoli kill.
It sucks when it's a new dish or you are inexperienced -- but if you can't afford practise runs where the result is allowed to be sub-par, then it's probably a good idea to switch to a different source of recipes.
Broccoli is really an edge case. The traditional measuring cup for the kitchen (looks like this: https://de.wikipedia.org/wiki/Datei:Messbecher.jpg) has more typical ingredients: semolina, raisins, flour, pearl barley, pulses & so on.
Grams of protein per ounce of food seems like a good example of this.