(Back a few postings)
Clipping a short on the way up *doesn't* work that conveniently if you have a 'not long', short cowstail. Hence the general continental thing of having a relatively 'not short' version of same (see the Petzl Spelegyca for instance)
However, for those who choose not to commit to long dangly cowstails - a small, especially keylock karabiner should reach the maillon, or at a push the loop of the knot (harder to use if it's loaded, keylocks help with this). When going past, unclipping is easy of course, as the rope (normally!) won't be loaded below the rebelay at that point.
Why bother? Well, I'd suggest it's a question of strength. If you can't rest on anything on an upwards rebelay pass, you're committed to getting your weight on the upper rope as soon as possible while standing in your footloop, while your stregth lasts. Hard if it's free hanging, very hard if there's lots of slack to pull through from a long hang on the upper rope. (You can, of course, transfer hand jammer across first while sitting on your croll on the lower rope - but this presents difficulties too on an offset hang, or if under an overhang). Passing a hanging rebelay, carrying a couple of bags on a long trip, while you try to keep balance on your footloop, and try to pull slack through your croll at the same time; not good.
Getting a rest (using short, or indeed long cowstail - if it ain't too long) at this point is pretty useful and frankly efficient - you can get it right first time because you're not in a rush. Clipping into the rebelay loop only, rather than the bolt, connector, or knot, generally won't achieve this.
It's a technique especially valuable for the unfit, those with less upper body strength, and those getting on a bit. That's why I like it.. The young, fit and strong can do without it - for now.