Given that you are already using degrees, arc-minutes, and arc-seconds in your specifications of latitude and longitude, it makes sense to use a unit of distances that meshes with them. Using meters makes less sense because it doesn't work well with the size of the Earth.

Difficulties with measurements and conversions are like a dead cat under the carpet - no matter how you push it about there's always an inconvenient lump and a bad smell. The Earth is inconveniently shaped, and you simply have to deal with it. The existing system of measurements may offend your sense of taste, but it has evolved over time to be useful to those who have to use it. Attempts to devise systems a priori and without taking into account the extensive experience of those who actually use them have always failed.

There's probably a reason for that.

I think "natural" was meant in the sense "it naturally follows" or "it's natural to assume", where it's meant to imply a natural path given your preexisting knowledge and conditions, not natural as in "this comes about in nature".

With that in mind, 360 is a fairly natural way to segment a circle for modern Humans.

60 is a very natural number.

You have twelve joints on the fingers of one hand. (Use the thumb to count.) You have five fingers (including the thumb) on the other hand to track multiples of 12 with. Voila, 60!

360 and 60 are quite handy, by virtue of having a lot of integer divisors. For a civilization where long division is unknown or limited to a few scribes, being able to divide things by common fractions easily is an important criterion in a system of measure.

> since it is related to 10 fingers

If your parent comment is correct. 10 finger thing will merely be an afterthought.