Weaponskills are like limit breaks, yes, we get that. But as has been several times, weaponskills can be spammed repeatedly in FFXIV, 90% of them don't do much more than a regular attack, and most of the animations are fairly lackluster. There are a few cool ones, but what the OP and others are asking for is something that transcends the limits of "weaponskills" in FFXIV.

A "Limit Break" in FFXIV would be something that charges up very slowly, on a bar separate from TP. Imagine in the UI you have one long bar situated under your HP, MP, and TP. As you perform class-specific actions (such as healing for CON/WHM, taking damage for GLA/PLD, dealing damage with weaponskills or magic for PUG/MNK, THM/BLM, and LNC/DRG, and buffing/debuffing friends and foes for ARC/BRD) this long bar fills up very slowly. It doesn't deplete when you exit battle/active mode, and the gain is designed so that every class can build up their "Limit Break Gauge" at about the same speed. Maybe it takes about 45 minutes to an hour to fill the gauge in normal circumstances.

Now, once this bar is filled up you gain access to one or several moves which are appropriately more powerful than any of your other weaponskills or spells based on the difficulty involved in accessing them. These won't be overpowered moves with effects like "Kills any enemy in one hit" or "Negates any and all damage for the remainder of the fight." It'll be stuff with situational use. Stuff that can get you out of a tight spot when you bit off more than you could chew, or help you take out the last 10% of a tough boss. Maybe a lancer could instantly get 3000 TP and have the TP cost of all weaponskills halved for 30 seconds. They'd have to balance that power with their enmity to avoid getting killed in the process, and so it all balances itself out.

Nobody wants to get rid of weaponskills. We want something truly impressive to use every now and then. When you can spam Doom Spike and Concussive Blow and Red Lotus every few seconds they lose their luster. They're good moves, maybe, but they're part of your normal arsenal. A Limit Break is NOT something that is part of your normal arsenal. It's a special attack that you'd only want to use in special occasions, and which you have to build up in order to access. The majority of your combat ability would still fall on your regular attacks and weaponskills.