The first boss battles in Final Fantasy IV to Final Fantasy VII, at the very least, had moments where you had to stop attacking, or the boss would counter with a powerful attack - this is signified by the boss changing in someway (e.g. becoming mist, closing its wings, etc.) and at least at times, you are even told by the characters to stop attacking at this point (not very coherently in FFVII, in the opinions of some.) I am not sure if this type of battle is ever seen again in any of these games (FFIV and FFV both have a later battle where you have to not attack, but it's the whole battle, from the begining), but if they don't it's kind of strange, thinking about it.
I mean, this is the first boss battle for each game mentioned - you've at least encountered regular monsters before this, and if you've thought them, you've gotten an idea of how the battles work, but then something different happens; you find yourself facing a monster that is not only more powerful, but there's actually a moment where you have to think and be patient with your attacks, with the game holding your hand enough by informing you of this. This could be a way of letting you know that not every battle is straight forward, that there could be a moment where you have to stop attacking, but this time the game doesn't have the characters point it out, and trusts you to remember the first battle and to use your eyes to check what the enemy (be it boss or regular monster) is doing.
But to my knowledge this never got used beyond the first boss each time - you still have to think of what attacks to use at times, such as casting the wrong element, but this doesn't usually put you in any danger, other than what is already present - it just heals the enemy or does insufficient damage. The only other thing coming to me is Abadon in FFVIII, but that also doesn't count, because the only problem with attacking when it's standing is that it's harder to damage, it doesn't counter with anything, and FFVIII doesn't start with a boss that follows this rule anyway (Abadon is not the first boss by any stretch of imagination.)
Feel free to say if I've missed any enemies that do have a moment where you have to time your attacks carefully, especially if it's in a game where the first boss followed this rule. Like I say, it would have been a good way to prepare you for the fact that some enemies were like this, if it had appeared beyond the first boss...