If you're just counting a small number of sheep and dividing them between yourself and your two brothers, I agree that divisibility by 12 is convenient (but what if you have 4 brothers).
As soon as you go to larger numbers and fractions, which mean the use of a positional system (which, BTW, has nothing to do with metric), i.e., number 523.23 means 5*100 + 2*10 + 3*1 + 2*0.1 + 3*0.01, and do mathematical operations, you have the same "decimal point problem", regardless of the base you're working in. In base 12 you might have a number like 3AB2.A9, divide it by 100 (i.e., 144 in decimal), mess up the decimal point position and be off by a factor of 12 - so you'd actually make a bigger error.
But with metric you have a great advantage that you can easily convert within a great range of numbers with very simple operations, e.g., metric tons/cubic metre = kilograms/litre = grams/cubic centimetre. Try converting between tons/cubic yard, pounds/cubic foot and ounces/cubic inch. More of less *any* conversion in the metric system is trivial, with only simple decimal point shifts.
Not to mention that as soon as you go above around 10,000 the scientific notation comes into play, so I can instantly convert 12.3 kilometres to 123*10^6 millimetres. Compare that with 12 inches in a foot, 3 feet in a yard, and 1760 yards in a mile... So, how many inches in 12.3 mile?
And BTW, binary is not as useless as you think. I can count to 1024 on my 10 fingers and to 32 with just one hand using binary. The latter I actually do sometimes, the former not.
Of course, one gets conditioned to whatever system they have been using since childhood and any system has its flaws, but, if someone tries telling me that having to know all the conversion factors listed on
United States customary units - Wikipedia, the free encyclopedia is easier and more convenient for calculations than the metric system, I will just laugh.