Earlier quoted context omitted.
I assume that the Sumerians were observant enough to realize that there were still a few days missing, and that 360 was better because it was a more divisible number actually. The Sumerians did, in fact, periodically insert intercalary months in order to offset the difference, which suggests that this is in part close approximation and on the other part nice for application.
I feel like unit debates often result from a misunderstanding between sides of "is perfect the enemy of good?" I thought it suspicious that they would have miscounted the days, but you're right: it's so dang useful that it's worth a little error (with occasional corrections) for such convenience. Of course, at some point it becomes a huge pain and you buckle down and choose something just as arbitrary but easier to h…
Even in metric-using countries, nobody uses it for time.
For actual applications of spherical trig though degree, minute, second makes a lot of sense, primarily because the earth rotates about one arc second every 4 minutes, and if you know this then you can do manual navigation via the stars and many other things.
However for many things I do use metric time, just not for the human aspect of it. For example, for one customer (admittedly in the sciences), we had to help them estimate how much hardware they needed for additional load. So you do the work in seconds because at that point the math is easiest, and convert to ratios following.