Why does modulus division (%) only work with integers?

You're looking for fmod().

I guess to more specifically answer your question, in older languages the % operator was just defined as integer modular division and in newer languages they decided to expand the definition of the operator.

EDIT: If I were to wager a guess why, I would say it's because the idea of modular arithmetic originates in number theory and deals specifically with integers.

Because the normal mathematical notion of "remainder" is only applicable to integer division. i.e. division that is required to generate integer quotient.

In order to extend the concept of "remainder" to real numbers you have to introduce a new kind of "hybrid" operation that would generate integer quotient for real operands. Core C language does not support such operation, but it is provided as a standard library fmod function, as well as remainder function in C99. (Note that these functions are not the same and have some peculiarities. In particular, they do not follow the rounding rules of integer division.)

I can't really say for sure, but I'd guess it's mostly historical. Quite a few early C compilers didn't support floating point at all. It was added on later, and even then not as completely -- mostly the data type was added, and the most primitive operations supported in the language, but everything else left to the standard library.

The modulo operator % in C and C++ is defined for two integers, however, there is an fmod() function available for usage with doubles.