nearly no high-level programming languages support it. Not even C

Sure it does. stdlib has the div family of functions, which return a div_t structure with quot and rem fields

Such an operation would be invaluable for things like converting seconds to hours, minutes, and seconds, binary to decimal conversion, or base62 encoding, and it's essential to any kind of rational (as in fractional) data type. With modern languages that support tuples I think it's a shame that we have regressed to writing two expressions to extract both components of what is essentially a value pair

This is similar to the characteristic/mantissa pair which form a logarithm (and is in some ways the exact same issue). It would be frustrating to have to call charac(15) to get 1 and mant(15) to get .1761, and the same is true of integer division