I seem to remember from one episode on History channel of the aliens or something that somewhere the 12 base counting was used and made sense because you count with your thumb the inner parts of your fingers whete each has 3 parts.
There are many different bases around the world, to think all of humanity uses base 10 because we have 10 fingers is wrong. You can count with the spaces between the fingers (base 8) for example
Someone else who knows how to finger count in base-12 and binary!
I think the binary one I learned as a joke, show someone they are number four.
The base-12 was an explanation for how the ancient Sumerians finger counted, using the other hand's fingers for groups of 12, leading to base 60 (5×12).
I have the same problem with binary counting practically though, and using a modified Sumerian system (both hands to 12) gets you to 144, which is plenty for anything where finger counting is actually useful.
One other thing, I use the finger bones rather than the knuckles, little easier but same idea.
There are a great number of ways you can count on fingers. You can easily support base 4, base 5, base 8, base 10, base 12, base 16, base 19, and even higher (144, say) with finger counting. There's nothing particularly "natural" about 10.