The division of the sky into 30-degree gores was Babylonian. The naming of each gore by a particular constellation came later. The Babylonian number system worked in multiples and factors of 60, so 12 divisions with 30 degrees in each was a neat arrangement. The fact that the sun moved by about one division in the time it took the moon to make a complete circuit was merely a nice coincidence. But it isn't exact and can't justify the division into 30-degree sections.
The naming of the sections by constellations came later. The list of 12 constellations is newer than the division of the sky. For example, the constellation of the scales didn't exist, and those stars were consider to be the claws of the scorpion. And of course the sun travels through the snake holder. So the division is not based only on the constellations that the sun passes through
Babylonian astronomers chose particular stars that were at 30 degree intervals, and then measuring relative to these stars. So they might say "Ahead of the rear twin (Pollox) by 10 degrees." The constellations that contained these reference stars then became the 12 zodiac constellations (which is why the snake holder got left out) And since two stars came from the scorpion, later astronomers split it off from the rest of the scorpion.
This system gives a basic framework for describing the ecliptic longitude of a planet. But it is unsuited to the accuracy required for modern astronomy. So modern astronomers use numbers for coordinates, fixing the coordinates to the position of the vernal equinox, and have dropped the constellations as a coordinate system.