Technically that would be the same as upgrading to a unit that requires a resource, but with the same unit graphics

I think that would be super-confusing and annoying: "unit X" of Civ A is stronger than Civ B but in case of "unit Y" it's the opposite (Civ B's unit is stronger than Civ A).
Why would it be confusing? We already have that with every other promotion in the game. I fail to see how having a promotion that says +1

or +20%

vs units with other promotion would be that confusing to anyone who can master +X % vs unit type which is common.
Even the +1

isn't as big of a deal as it sounds. +1

is about equivalent to +20% for most units and that's the same as Strength 2. Or in some cases such as Knights and Maceman Strength 1. And having a promotion that adds free Strength 2 or Strength 1 vs units with inferior resources is hardly overpowering.
Basically I think it would be nice if you could build all units that currently require Copper or Iron with either. And than you have ALL units including those that don't require resources to build from that era (so obviously not gunpowder) that have Iron get a bonus vs Bronze. Not huge, but enough that all things being equal Iron gives you an edge. Something like maybe 20%. That way you wouldn't get a situation where a unit can beat it's direct upgrade. But at the same time you would get situations where having superior resources does extend the reach of your new units and the longevity of your old ones somewhat.
Like say we take the Spearman and Pikeman as an example. Spearman is

4, Pikeman is

6. Even with the 20% bonus the spearman is still just 4.8. Or 5 with a +1

. Same difference. So it's not enough to beat the pike strait on. And it's not going to be doing the job of Iron Pikes vs cavalry either. It's counterpart being the

10 knight. 8 vs 10 is still not as good as 12 vs 10. But if you have a bronze knight and an iron spear than it becomes 9.8 (or 10) vs 10. Still not as good as the pike but now much more relevant. Which means you won't get so easily overrun by new units.
That's basically how it works in FFH in practical terms. And there it really works to add an extra layer of strategy to the whole thing and an extra reason to rush Iron Working and fight for Iron instead of waiting for the AI to trade it to you. Especially since it applies to all units so stuff like Iron Longbows are a thing.