If you go down this rabbit hole, you will eventually realize that it is our base 10 number system that is weak in terms of divisibility. If we counted in base 12, the metric system would follow suit and you’d have your convenient fractions.
In my “perfect world” musings, however, I jump back and forth between base 12 and some power of 2 base. The latter would not be very naturally divisible but would make basic arithmetic much easier. There is a reason computers prefer binary.
The other point I’d like to raise is that even in the imperial system, you are not spared having to deal with awkward fractions, as you will realize when you walk into a hardware store looking for that 5/64" screw. Apparently, fractions are not a deal breaker in this case, so perhaps we should refer to a third of a metre as simply that: 1/3m?