Let's say I have a plenty of supply of diamonds for my archer's arrows and my blacksmiths can easily work with diamonds.
Would diamond arrows be superior to iron arrows?
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Diamond is brittle. It is hard (resistant to scratches) but not tough (resistant to breakage). So the diamond arrowheads would be no better than flint or obsidian arrowheads in this regard. This makes your arrows a consumable. Once fired the most likely case is that the arrowhead is broken, and needs to be replaced even if the shaft and fletching are still intact. Whereas iron arrowheads may be only dulled.
No, they would be far worse, diamond is dull and brittle.
Diamond cannot be made sharp like flint or obsidian, diamond has a regular crystalline structure, but flint is a amorphous glass, it has no crystal lattice, so it forms conchoidal fracture, which is what gives flint and obsidian such super sharp edges.
As Nate pointed out it is also brittle, so it will not be any stronger either. There is absolutely no benefit.
There is one use case I can think of for diamond arrows, and it's not really something you'd find in the real world, but you might be able to create some "trick arrows" like you see in shows like Green Arrow or RPGs like Dungeons and Dragons. If, for some weird, contrived reason, the materials for glass are so hard to come by that it's cheaper to use diamonds, you could create diamond casings to put behind your arrowheads and add poison, acid or other dangerous fluids in them. When the arrow hits, the casing shatters and whatever is in the container is released.
Poison applied directly into a fresh arrow wound is extremely dangerous because it directly enters the bloodstream. Acid can inflict hideous injuries and might be usable to damage larger objects that you otherwise would do little damage to with an arrow. Depending on the tech/magic level, you might be able to create 2 somewhat safe chemicals that when mixed combine into something explosive and/or highly flammable. There might also be chemicals to suffocate small flames, but I don't really know how feasible that is.
Technical reasons aside, I think this would be a very bad idea. Once it became known that your kingdom could afford to spend well over $1000.00 per arrow, you would open yourself to invasion by every other kingdom - that is presuming that diamonds are as valuable in your world.
I remember reading a story once about an Indian tribe that, not knowing its value, began to fashion bullets using gold. That tribe was entirely wiped out soon afterward.
Greed is a very powerful motivator.