Indeed, maths never "decreed that sine and cosine have to take radian arguments". But thinking that makes any sort of point is a fundamental misunderstanding of maths.

There are infinitely many sinusoidal functions out there. You can just adjust amplitude, frequency and phase to your heart's content.

Trigonometry basically requires that sine and cosine have specific amplitudes and phases, but gives not one shit about how you map angles to frequency. Degrees are completely arbitrary, but both radians and turns have pretty natural definitions, with turns indeed being the easiest to work with. So far so good.

Calculus does have an opinion on frequency, though. There is exactly one non-trivial pair of sinusoids s(x) and c(x) where c'(x) = - s(x) and s'(x) = c(x), among a bunch of other very useful properties.

When you put calculus and geometry together, s and c are have the same amplitude and phase as sine and cosine from geometry, and the two pairs are exactly the same if you match the frequencies such that the argument is the angle measured in radians. It's just so damned useful to use angles in radians and make everything play together nicely.