The advantage of a non-tele long lens is exactly as you say: fewer elements. I have a 400 mm M42 lens that has only three elements: the achromat doublet at the end of the tube, and the simple meniscus behind the aperture. A 400 "tele" would be much shorter, but it would have additional elements to change the effective focal length of a much shorter-focus objective set. For instance, there might be a four-element Tessar type, with independent focal length as short as about 200 mm, with aperture in the middle, and a three-element achromatic negative group near the mounting flange, to make a "400 mm" telephoto that's only about 240 mm from film/sensor to aperture.

Along with fewer air-glass surfaces, simpler lenses are also much less expensive to produce to high quality -- my 400mm triplet has only three pieces of glass, and no glass-to-glass cemented joins, while a tele-Tessar has seven elements, and three glass-to-glass cement joints (assuming the focal extender elements are a cemented triplet, as is often the case with quality ones).

The other side of this is that "simpler" long lenses are often seen and treated as "bargain" optics, so they don't always receive the level of quality control you might get in a lens that will be offered at a higher price (perhaps because it's shorter and easier to handle). And even though lighter in actual weight (due to much less glass), they may feel heavier because all the glass is as far from the camera body as it can get.