There certainly are thirds, even if they are expressed in scalable percentages.
There are 33%, 66% and 67% percents, but as repeatedly stated decimals just don't divide into thirds cleanly, there are no thirds in the 3 feet to a yard sense. Point being that even division just isn't that important.
It doesn't come up as much in daily life..
I suspect what "comes up" and doesn't is quite dependent on what is easy to do. I find myself calculating the volume of containers quite often, it is very handy when adjusting volumetric yield sizes to pans/containers. I could measure the capacity by pouring water of course, but why mess around with that if your measuring system has the tools built in? I was not very pleased when trying to figure out how many cubic feet of soil it would take to fill up a tote with the volume given in gallons. Neither are the units related, nor is it easy to convert between cubic inches to cubic feet (unless you are well versed in cubic duodecimal calculations).
The thing about the customary measures is that they evolved with the uses they are put to. They are the result of what people found most useful rather than what was prescribed.
That's not really a fair description. Considering the plethora of contradictory standardized and customary units that were floating around before metric alone makes it questionable. The fact that many contradictory versions of the "same" units were in fact mandated at various times and places outright contradicts such a claim. I'd say it's more fair that customary measures are units that some people, at some point, found useful for their particular tasks and were subsequently adopted for broad usage via network effects.
That's the reason I keep beating the "arbitrarily precision" drum. When you have a system where conversions are easy, you can adopt whatever approximations are useful for the task, instead of dealing with someone else's foot or stride you can have yours and retain all the advantages of a cohesive measurement system with a few basic calculations. If the size of the standard 12 inch foot makes sense for your task and clean division by three is important, then there's nothing wrong with working in 30 cm increments (or 3 dm, if the task scales up more than down).
It is a useful intellectual exercise to consider a metric system not based on ten though. It would retain the natural cohesion between length and volume (and mass for for water). but might use halves and thirds rather than tenths.
Oh, absolutely, however I'd go for an all out base 16 change across the board. As I said, for practical purposes (1) approximations of repeating numbers are adequate as long as the system easily supports arbitrary precision, (2) there will be repeating numbers no matter what, (3) binary divisions are the only inches easily eyeballed and performed without a lot of fuss and/or special equipment. For example, high precision division of weight is very easy in a base 16 measurement system, whereas any base divisble by three is as problematic as decimal.
Sounds like rounding to millimeters would be plenty accurate then.
There are no thirds in serious baking, it's all decimal in the form of baker's percentages that can be used with whatever weight units you want.
I'll note that it would probably reduce headaches quite a bit if the foot was removed from the yard/foot/inch equation, as it stands 3 parts is the only thing the yards divides evenly to for the next smallest unit. I'd rather deal straight with 36 inches, of course most people have decided to go the other way and ignore yards when inches are in use.
Overall yards are a prime example of the problems with US customary units: inconsistent divisions. Commonly used lengths go from 1760 to 3 to 12 to binary division (so there are common factors, but the bases don't normalize until you divide inches), and miles are usually given in feet, not yards to top it off. Plus I believe there are random sub-inch units, but I don't know how they fit, or don't fit into this "framework".
Then there's the lack of cohesion with dimensions and volume/weight disconnected. Volumes are at least mostly (ah, teaspoons) consistent with a binary division, however the individual divisions have names, half of which have been forgotten. So people learn seemingly arbitrary conversion factors between ounces and cups and quarts and gallons without knowing the underlaying system.