People are probably thinking "fuck it, let's go with the upheaval! Let's get rid of the silly base 60 system!". Ok then. First, we could divide the length of a year into 100 days. Wait, no, that has to be 365 because otherwise the seasons would get out of whack.

Ok, but we could definitely have 10 months right? They did that before. Perfection. So every month should have exactly ... Uh 36.5 days... fuck

Well, how about having 10 day weeks? Shit. Same type of problem.

Fine, let's ignore months and weeks. What about the 24 hour day? Instead, we could break the day into 100 units. Each unit would be 14.4 "old minutes" long. That seems fine. You could subdivide that into 100 subunits, each of which would be about 8.6 "old seconds". To keep things reasonable the final divisor would be 10, so our new short "human counting" units would be about 0.86s. Groovy. Pity that years, months and weeks don't work out.

So why are there "really" 360s in an hour? Probably for the same reason that there are 360⁰ in a circle. Early astromomers and mathematicians probably thought that the universe was a perfectly created system. They likely modelled dates and geometry on earth's annual journey through the sky, but we're a little bit "off". Like how the months are supposedly lunar. We only discarded the idea of perfect celestial spheres relatively recently.