Having prepared many a baked good in the U.S., I can honestly say I've never read a recipe that calls for 'sticks' of butter as a unit.
The 'cup' measurement is still not a problem though - because the stick-of-butter packaging tends to have little lines telling you exactly at which point you've reached half a cup, a quarter cup, 1/8th of a cup, or tablespoons, etc.
It's because the U.S.'s food industry is so homogenized that the volume measurement 'works'. 1 cup of product X from one company is going to be equal to 1 cup of competing product X from the other company.
There are some notable exemptions.
Brown sugar, for example, which is why most recipes will call for "1/2 cup of brown sugar, packed" - because if you don't 'pack' it, the size and shape of granules can greatly affect the actual amount.
Cherry tomatoes was another example. But the thing with that, and with many other such items, is that the exact amount doesn't really matter all that much - it's certainly not 'scientific cooking'. So one time your pizza / salad / whatever will have a bit more/less tomato than the next time, but it's not a big deal.
Eggs is a huge one. If a recipe calls for '8 large eggs', have a good look at the 'large eggs'.. they're far from the same size. Nobody bothers to suggest that one needs X milliliter of eggs, though (never mind separating out yolk from egg white).
Onion is another one. Recipes often call for '1 large onion'. Go to a grocery store in the U.S. and check out the large onions.. there's some the size of a big nectarine, and others are easily bigger than your fist. So which do they mean? It doesn't really matter... use the latter if you like things more onion-y.
Only when measurements are very strict, a recipe will in fact call for weight.
Personally I think it makes cooking a lot easier - except for when you get to the whole 1 tablespoon = 3 teaspoons vs 16 tablespoons = 1 cup thing. Having a measuring cup/thing for every common cooking unit saves a lot of mess, especially when you need to double/triple/quadruple recipes.