Your intuition that it's due to the sound relationship is a good one. It's an "easy" transition for a listener, because the relative major and minor scales are built from the same basic set of pitches (notwithstanding some standard alterations in minor, like raising the seventh note to provide a leading tone).
There's also a historical reason. As major/minor tonality developed, instrument tuning was also developing. On keyboard instruments, for example, it simply wasn't possible to play in all twelve major/minor keys. Especially before Bach, composers generally had to stay within the boundaries of closely related keys, like tonic/dominant, tonic/subdominant, and relative major/minor, because the instruments couldn't manage other kinds of modulations. Classical-era composers had more flexibility, but it's not until the Romantic era that composers are able to fully stretch out and regularly use distantly related keys.