You're right! Since Iron is in most fertilizers, NPK and lime are the most critical factors towards greening up the lawn (actually, water is, but that's a different story).
Professional athletic fields and golf courses will use a liquid form of Ironite to maintain that unnaturally dark green that those guys are paid to maintain. However, Iron only greens up grass for so long, so it's really just a temp fix. Those guys have big budgets, so they're not afraid to spray it regularly.
The bottom line is that Chlorophyll makes grass green, not Iron. Iron, along with several other elements in the soil contribute to the plant's manufacturing of Chlorophyll. As long as your fert program is well-balanced with the essential micronutrients you should be fine.
That being said, if you want a quick green for a specific reason, say, for example, the customer wants a really green lawn in time for Memorial Day, then, yes, Ironite would be a quick fix. But otherwise, you're wasting your time.