I would like to suggest into alternative options that uniforming units speed to improve balance. I doubt that removing units differences would make the game more interesting. I personnally think that balancing the game should be about giving options to players to deal with a specificity rather than removing them.
For example if you want to maximize the productivity of your soldiers, you could build a barrack near your minerals and use this particular one to produce the slower soldiers of your army. Those will then collect only minerals as the walking distance for this particular task is constant and usually smaller than for wood. To reduce the economic disadvantage of walking speed, players could build more dropsites, use elephants or the carrying tech. Those tech still remain largely unused by a large number of players even when wood is sparse.
Also, in early game, most civ don't offer the choice between different ranged units. So the economic advantage that might offer one ranged unit with respect to another plays no role in the way players will act once the game has started. It only affects balance accross civ which seems to be a different issue. Archers are definitely at a disadvantage with respect to other ranged units but taking off their economic disadvantage would still not solve their problem. Giving them some advantages as also suggested by Philip the Swaggerless would make more sense. About the question of speed, I think that raising the speed of melee units with respect to ranged units remains interesting.
One reason to prefer ranged units over melee units is that during a fight, they are much more effective in killing. Ranged units can also be more easily managed, you basically just need to group them behind their meat shield and press H to be sure they target the closest units. Melee units are more tricky, the closest units is sometimes a bad target for them. All of them might be running toward the same unit which is either isolated, either moving in the opposite direction. Melee units used offensively can spend a good amount of time walking around during the battle before dying while still ranked I. Increasing their speed slightly might give them a chance to kill something before dying. Currently, only swordmen seems to make sense as a weapon on the battlefield in the absence of cavalry units. They are the only melee unit that can get decent kills, other units are too slow and weak. Many civ do not have any and metal scarcity often is a good reason to keep them out of the battlefield. Raising melee units speed could also potentially reduce slightly the problem of rams too fast to catch.