It's not that a system based on base 6 would be strange. That'd be a logical system, too. Just as any other system that consistently uses a particular base.
However, a system that uses numbers of base whatever but then proceeds to jump from one unit to the next one in completely arbitrarily sized steps such as 3; 22; 10; 8; 3 is illogical in any base.
Mostly because it's very easy to make calculation on base 10.
If i ask you to tell me how many millimeters are in 5.7 meters you could probably reply easily without a calculator.
You probably wouldn't do it as easily if it wasn't base 10
We define 1000 mm as one meter as we are base 10 centric. If we live in a base 8 world, we would have define 8x8x8 mm as one metre and the answer to 5.7 m base 8 would be 5700mm base 8 too
It's not fundamentally easier to do calculations in base 10. It's only easier for us because that's what we learn as children.
If our number system was based on a superior base, like dozenal or senary, we would be able to do calculations on that base easily and would find working in tens awkward.
That's literally the same way with any other base. We just defined orders of magnitudes to be multiples of 10 because we use base 10. We could just as well have used other multiples.