This story gets complicated because there ARE Ludwig kits that have 18 X 14 inch bass drums. But, the Jazzette, specifically, has the shallower 18 X 12 inch bass drum.
I have seen more than one or two small Ludwig kits that have the 18 X 14 bass drums and they also many times have a bass drum mounted cymbal holder and an offset rail consolette. These factors set up an "argument" (so-to-speak) as to whether or not that kit can be called a "Jazzette" or a "Downbeat". Because a Downbeat has all those things described in the 18 X 14 setup, too -except for the 20 inch diameter. But other people just go by the bass drum diameter and call anything with an 18 inch bass drum a "Jazzette".
If you go by the "official" word, then a true Jazzette MUST have the 18 X 12 in bass drum, a center-mounted rail consolette and not have a bass drum mounted cymbal mount. But, having said that, there are always exceptions. For example, a true early Jazzette MUST be natural maple or natural mahogany finished shells. But, I have YET to actually see a mahogany Jazzette -the model they used in the catalog. One forum member here has seen one, but there are no pictures of it. So, the truest Jazzette kits are extremely rare - I mean extremely rare! And to find one in excellent condition that hasn't been "tampered" with or "customized", is even rarer.
Ludwig wasn't the popular bebop drum company. That honor went to Gretsch. So, rumor has it that Ludwig didn't sell too many Jazzette kits, overall. That's probably another reason you don't see too many floating around and being "recycled" on EBay. They simply are a very rare model of drum set in the real world.
In 1976, Ludwig changed their 3-ply shell layup and, in addition, quit advertising kits with 18" bass drums. As described, it was likely economics of the day. They just weren't big sellers for Ludwig at the time. 20 inch bass drums (and larger) were better sellers for Ludwig.