Only in certain fields. For most interactions divide by 10 is far easier than divide by 12, and you'd end up with far, far more "eyeballed" measurements.
I hope you're comfortable with changing literally every number in society to base 12. My house cost $42A765_12. My SSN is 399-AA-5866 and phone number is (289) 257-B84A. The distance to the moon is actually 50A693_12 feet. I used the additional symbols A and B as per usual notation, but it's okay if society agrees on some other symbols for the extra two digit values.
If you don't make the base of the number system agree with the base used for converting between units, then conversion becomes so much harder. For example, it's not immediately apparent that 204 inches is 17 feet, but it is immediately apparent that 204 cm is 2.04 m. Furthermore, when the base disagrees with conversion factors, you run into issues like variable-length fields - like, "2ft 9in", "2ft 10in" (notice the inches transitions from one digit to two digits).
Possibly yes. But every implementation of base-60 I've ever seen is actually implemented as alternating base-6 and base-10.
A true base-60 would have 60 unique symbols for the different digital values, much like how in our set of ten digits {0123456789}, none of the symbols have any rhyme or pattern with respect to the others.
Good luck memorizing the ~1800 entries of the base-60 multiplication table.
Base 12? That's a small number. Now base 13? 13's a big number. The biggest number, perhaps. That's what they're saying at least. Base 13, 13 colonies, now that's America.
This can make sense for currency, but units of weight and distance and so on are infinitely divisible. You can just have a third of a metre if you like. Or 333 mm if the inaccuracy is acceptable. And so on.
And it's not like 1 is some special value. If you start from a base of 120cm you get enough even divisions that you rarely run into the need for fractions
Unless everyone worked in base 12 numbers too, that'd be a mess. Part of the beauty of metric is how often calculations devolve to shifting the decimal point.
No, converting units is not a useful exercise. airplanes are measured in mm - even the full length is in mm not decameters or even hecameters (i had to look those prefixes up, spellcheck doesn't even know the word, but I think they are correct)
Vehicle drawings (maybe mechanical engineering in general) might be in millimetres, but a lot of civil engineering works in metres, so when designing some bit of infrastructure to fit certain kinds of vehicles, I do need to convert between the two, and the easier, the better.
You can actually count to 12 on your fingers using one hand. Use the thumb as a pointer, then for each of your other fingers you have three joints. So 3*4=12.
It's hard to actually count using more than 4 bits/hand though. The quickest methods that require the least dexterity are those that count the knuckles (which are actually used in some counting traditions, unlike binary finger-counting).
So no, as a human being, I'm fine with base 10.