There is always going to be *some* damage cap, because it's unfeasible to create game code that supports infinitely large numbers. However, it is pretty easy to make damage caps that are for example 100 times higher than what you can hope to achieve with every single piece of awesome equipment in the entire game, making the "cap" practially unreachable, meaning no one will notice that there is a cap.

And we do not lack an FF game with this. FF11 is a game where normal attack damage is around 100-800 damage, special skills range from 1000-8000 damage, and the damage caps at 99999. Even in special cases where you do extremely much more damage than normal (only doable with extremely rare and expensive one-time-use items, or on one single boss which takes extreme damage under special weakness circumstances), you usually don't get very far past the 50000 damage mark in a single hit.

Additionally, HP and MP is in the range of 900-2200 depending on job and race, while the maximum HP/MP is not 9999/9999. In fact, the HP/MP cap is unknown, but people have managed to get 10500 HP on a character, just as a test, so it is likely that that too caps at 99999/99999.