Would there be an advantage of doing your reps only in the bottom half (stretch) over doing your reps with a full range of motion?
Would the advantage be related to mechanical tension, muscle damage, metabolic stress or a combination?
the occlusion effect. Give it a google. Also if you are trying to bring up a weaker body part and want to focus tension on that
I think it might largely depend on the exercise and the goal of training. For example, some exercises lose tension on the targeted muscle beyond a certain ROM (think of the Bench Press where it transitions from Chest to Triceps as you get further in the ROM, although there are plenty of other examples)
Some exercises that have a arc-shaped ROM also have this problem. DB Flies for example, the upper 3rd is almost completely horizontal and does almost nothing for the chest, so only doing the bottom 2/3 is a good option (this is corrected largely with Cable flies however, so the choice of exercise is quite important as you can see)
Standing BB Curls are another one. The tension shifts from the bicep to the front delt as you go through the ROM unless you take care to keep it on the bicep (using hand position and body position a la the Gironda Perfect Curl would be one way)
They can also be used for a specific purpose as Yogi mentioned above. Coach Christian Thibaudeau Uses then in a 5-5-10 method (similar to 21’s using 7-7-7)… 5 bottom partials, 5 top partials, then 10 full ROM. The partial reps occlude the muscle and then the full ROM reps make the muscle work in the hypoxic state which builds up metabolites. This doesnt work for every exercise though, as the muscle must be under tension for the full ROM (DB shoulder Presses, cable tricep press downs, cable BB curls are all good choices here)
It probably has almost no meaningful use (and might even be detrimental) for powerlifting/oly lifting where higher numbers and speed are the training effect you are after.
So yeah, I think it does have certain uses, But to use only bottom partials as your only means of training EVERY exercise is probably short sighted at best, and could be worse than regular reps depending on your goals and the exercise.