One benefit of base 12 and base 60 over base 10 for everyday use with things like time is simple factorization. You can divide 12 hours evenly into halves, thirds, quarters, and sixths, and 60 minutes evenly into halves, thirds, quarters, fifths, sixths, tenths, etc. With base 10, you've just got halves and fifths.
A base-10 unit circle would be abhorrent. 1/2 of a circle is an important concept, but 1/5th and 1/10th of a circle are rarely used in geometry or trigonometry. Meanwhile, a right angle (1/4 of a circle) would require an ugly fraction, and the angle of an equilateral triangle (1/6th) would require a repeating decimal.
Think of 12-hour clocks and 360-degree circles as paper bags. When we're fucking with angular concepts, you do not want to take those bags off Decimal's head.