In short, you can't take just base units and multiple them together to get a Litre.

What I mean by that is that in order for a unit of volume to be coherent with SI units it would have to be ONE meter times ONE meter times ONE meter. Not 1.5 meters, not 0.1234232 meters. Not any other amount of meters besides 1. And the same would go for any of the base units (second, kilogram, amp, kelvin, mole, and candela) and deriving a unit from them.

With a liter you going 0.1 meters times 0.1 meters times 0.1 meters.

This means that the "coherent" unit for volume would be a cubic meters. The thing is that's... a really big volume so we just don't use that day-to-day.

There are of course plenty of other derived units that are coherent. Like newtons, hertz, etc.