This is absolutely not cheating. When you start instanced content, your abilities cooldowns should be refreshed. End of conversation. Starting a leve and abandoning it to reset the cooldowns is merely a workaround for the bad design of the instanced content.

If cooldowns can be refreshed before leves (instanced content) than they should be automatically refreshed before Ifrit, Gardua, Cutter's Cry, etc (also instanced content).