If this was a game like WoW, a skill that's used "in time" would be anywhere before the moment that it is absolutely required.
For FFXIV, to use something "in time", you have to take into account the preparation action animation.

If you fail to account for it, you did not use the skill in time.

Case in point, the tank LBs are instant (at least up to level 2, never had the chance to use tank LB3).
Healer LB and attacker LB have that preparation because it was designed to have it.

Note the word "instant" in the skill tooltip refers to the cast time.
For some games, that means you press you get. But not so in FFXIV.
In FFXIV, you get a cast time, and before that cast time you have a preparation motion.
(Limit Break doesn't even have a cast time categorization on its tooltip, so it was never presented to be instant anyway)

Again, this is a design choice.

I have no problems with people lobbying to wipe this design out, it's up to the developers to decide.
But please don't keep saying "instant should be instant", because it is instant cast.
Please stop saying it is flawed or is bugged or due to server infrastructure or that "its common sense" etc.

Attacking the implementation is no way to lobby a change to a core design.