I think the 12" format was utilized to enhance the bass parts of the track to give it the 'disco' vibe.
To increase the bass elements, the stylus needs to move a little more from side-to-side and hence the width of the groove increases. Keeping the same space between the grooves, the total physical space needed for the recording is greater, hence the use of the 12" format. The total length of the entire track, if laid out in a straight line, would not be any longer.
Imagine coiling a piece of string around in a (7") spiral, and then increasing the string's girth slightly; the size of the spiral would enlarge, in proportion to the increase in the girth of the string. As the increase wouldn't be anywhere near enough to increase the diameter of the spiral by 171.428 %, it would not fill an entire 12" record.