I’ve always assumed it’s because of the usefulness in its divisibility, with 60 able to be subdivided evenly in halves, thirds, quarters, fifths, and sixths, and because 24 is just 12x2 and 60 is just 12x5, that remains the case (save for fifths) for all subdivisions of the day in its 60/60/24 configuration.

My guess is that it’s simply an issue of working with something like a day, defined by cosmic forces rather than human sensibilities or control, where you don’t always get something that can be decimalized and still have useful units of time. I’ve done zero research on the actual reason, though, so that’s just a guess.

Also im aware that base is not the proper term in this case since the base is still 10, but I have not idea how you would call the switch to the bigger unit treshhold

Actually “base” is entirely the correct term in this case. The first group to write down a really systematic method for timekeeping were the Sumerians, and they used base-60 math. This worked really well with solar and lunar cycles, which were important for crop planting, and with astronomical studies (mapping the stars had major applications for both navigation and religion, so it was culturally significant). Empires that came after the Sumerians copied and expanded their system, so it eventually spread to everyone.