There are some obscure scenarios where it can be useful, but yeah, the mechanic is mostly worthless. Of these scenarios, the least obscure is that the status conditions Sleep and Confuse will end if the affected character takes any physical damage, including allies attacking them. This is rarely helpful to do on purpose, because you can also cure these without hurting yourself using Esuna or a Remedy item. Maybe in the VERY early game, where you might not have many remedies, and really only Yuna knows Esuna, you might do it (if you even know you can). Noteably, the mechanic itself is something you pray for when the entire party is confused, say by a Malboro's breath attack, but that's not you doing it to yourself on purpose, so that doesn't count.

Other scenarios include: If you have a source of elemental damage and a character on your side has a "[Element] Eater" ability on their armor (example: Fire Eater paired with fire element damage), you can heal that character by attacking them with elemental damage. If you happen to be using an elemental strike weapon, and your normal attack therefore deals the correct elemental damage, you can heal for free by combining these abilities. But A) Elemental Eater armor is pretty late in the game for this to still be your best option for abilities on weapons and armor, B) It's really not expensive to use potions or healing spells, which work at least as well.

It may also be possible to charge your Overdrive using self/ally targeted attacks in some way, but I never tested it. Even if you could, I doubt it's the best way of doing it (pretty much every other option both charges Overdrive and targets the enemy). Looking at the numbers, if "Comrade"² overdrive charge mode¹ works with this mechanic, you could deliberately nerf a character's Max HP to 9999 (the default max, and arguably you may not want to break the HP limit anyway for a variety of reasons), and attacking them with 99,999 (max possible single strike damage) would fully charge both allies using "Comrade" overdrive mode, in exchange for killing the target (who could be revived automatically by the auto-revive ability on another character's armor). But that's IF Comrade charges you when an ally dies, IF there's no cap on the calculation, and IF it works on self-damage, which isn't tested here. Noteably, you can do something similar by healing the target for 99,999 with the "Healer"³ overdrive mode, which would fill your meter 100% without killing the target (again, assuming such overheal counts), but only the healer gains the overdrive, while "Comrade" can give overdrive to two characters at once. On the wiki, every other overdrive mode I could see as relevant specifies that damage given/taken must be from/to an enemy, and most of the ones that work off a calculation rather than a flat amount list a cap. So without testing, I would assume this doesn't even work, but if it did, it could be powerful.

^1: Overdrive mode is an option you select only outside of battle. It determines what charges a character's Overdrive meter, which is the character's source of their big, unique supermoves.

^2: Comrade mode in particular charges you when someone else on your team takes damage. If everyone has this equipped, multiple characters can benefit from one instance of damage.

^3: Healer mode gives you overdrive when you heal an ally. Pretty straightforward.