So, this is JUST a theory, but I think I know exactly why you need Blaze Rods for the crafting recipe of the end-game item, the Eye of Ender. Maybe this is stupid, or someone already thought of this. Sorry. But here is what I think...

So, first let's look at the Enderman. They drop the Ender Pearls. If you didn't know that, I will be under your bed tonight with a knife. Just saying. But anyway, what ARE Ender Pearls? Their hearts? Their brains? Something else? We know it can't be their eye, because their eyes are purple, a Violent Violet one could say. I thought that it was something else. Maybe a teleportation organ/crystal? But, after thinking about it, I realized that there isn't anything hard about this. I just needed to READ THE OFFICIAL MOJANG BOOK ON THE END!!!! It's called "The End." I would actually recommend it, pretty good. But anyway, sense it's official, that theoretically means it's canon. LOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOORE!!!! This means when Mo says that the humans are "Ripping out their hearts," it means we're ripping out their hearts. Huh. One problem solved anyway. Ender Pearls are their hearts, we through them, we move through Space/Time. But... if we can just teleport like that... Shouldn't the Ender Pearls activate the End Portal themselves? Why do you need to mix in powder-of-hot-demon-monster-flying-pest-thingy? The easy answer is... Mojang needed an easy way to separate Ender Pearls from Eyes of Ender when the right-click function is called. But I refused to believe that. No WAY Mojang, the same company that forces its customers to fight each other once a year to pick one single mob, the people who aren't updating the End AT ALL, would do something like that to us. So I looked at the End Portal next.

It seems to me that the End Portal frames are devices made by long-dead races that were used to capture space energy to open the gates of the End. They all USED to be open, but the Eyes decayed over time due to being, technically, organic matter. Some lasted longer than others though, giving us a reason for the Eyes random chance of spawning in frames. Theoretically, though, why couldn't you just use Ender Pearls instead? They have much more teleportation/space magic, because you can throw them and they teleport you. So, having found no real reason for the Eyes thus far, I moved on to the last component.

The Powder-of-hot-demon-monster-flying-pest-thingy, AKA Blaze Powder, is one of three components of a Blaze. The other two are the head and the core. My personal theory is that the Blazes are automatons created to guard the fortress. I thought about the purposes of the Blaze Rod/Blaze Powder and came across a startling discovery! Every time they come up, it's for energy/magic! Shocker!

Conclusion? The powder is the power source for the Pearls, which aren't active unless used by a Player. Mixing the powder will trigger the space energy that the Pearls use, and slotting them in place in the frame will trigger the frame's purpose: the collection and use of this energy to generate a rip in space/time that leads to the home of the Pearls.

This has been: Science with Dr. Extreme! Send those checks to Extreme Drive, [​REDACTED]!