That lens (the 16-18-21mm Tri-Elmar) is a bit of an odd duck. It's an ordinary parfocal zoom lens in every way except one: it only has three strongly-detented focal lengths available to the user. It can be argued that this makes it easier to optimize the relationship between elements at the three available positions, but there is noless opportunity for wear and misalignment than there would be with a continuous zoom. The real reason for the lens being a Tri-Elmar rather than a Vario-Elmar is entirely to do with framing on a rangefinder camera. Without the detents, it would be necessary to have a viewfinder that zooms with the lens, probably an auxiliary finder. Whether you use an aux (hot shoe) finder with etched frames or the normal frame line sets in the rangefinder's viewfinder (which would be automatically selected by varying the position of the frame coupler on the lens mount) a multifocal lens becomes usable on a rangefinder without requiring a zooming finder as well.
Most discrete multifocal lenses, historically, were quite different. They were single, well-corrected focal length lens made in more than one part, and you could choose to leave one or more of the parts (lens groups) out of the assembly to get somewhat less-well-corrected lenses of different focal lengths. The original Symmar lens design is a good example of the breed—by removing the rear half of the lens from the shutter, you got a longer, slower lens (you still had the same iris, so the longer focal length meant a smaller relative aperture). It wasn't ideal, but the smaller aperture made up for some of the lost correction, and it was certainly cheaper than buying a separate, longer lens. Other multifocals came as kits, often with three groups, giving you three to six different focal lengths (depending on the design and how you assembled the lens). That's really only a practical (?) approach with large-format lenses where you have access to parts of the lens both in front of and behind the iris and shutter. And it's not entirely dissimilar in approach to the auxiliary lenses sold for cameras with fixed lenses.
With SLRs and other camera types having through-the-lens viewing/framing, there is no real advantage to not making a zoom. The mechanical couplings to adjust the relationships between the lens groups is not significantly more complex than it would be for a detented lens like the Tri-Elmar. And if the zoom range is kept as small as it is on the Tri-Elmar (just over a 1:1.3 range), then maintaining as high a degree of correction and recilinearity over the entire range would be just as easy.
