Ranged units are problematic for balance. Humans, you see, are very good at maximizing ranged power. The AI is less able to take this advantage. This is likely why standard bow weapons are so incredibly nerfed. I can use ranged units and retreat to the very back to get 2 strikes in before the enemy can catch me. That might seem powerful, but bows need to stand well balanced in normal tactics. That exploit is not a logical basis for nerfing. Let's look at the figures for bows versus staves, shall we? A shortbow takes a tech that only gives shortbows. That is somewhere around 25 turns on average to get a single weapon. The magical staves also offer a variety of other weapons, buildings and items. So you get alot more just from choosing the magical choice. The difference is that shortbows take only labor to build. That means you can mass produce them without having alot of resources.

Now let's look at damage. A shortbow does 7 pierce damage with -8 Initiative penalty. It weighs 10. A staff does 6 fire or ice damage with -6 Initiative. It weighs nothing. Compare this to the weapons from the prerequisite tech for bow, Weapons. You can get 9 melee damage with backswing from an ax at only -2 Initiative. It will take you a turn or two to reach the enemy, but in that time no bow units will have even fired. Add a wood shield to that and you have one powerful unit. In tests, 4 axes with shields and full leather beats out any combination of bows and axes. You do very little damage with bows against even slightly armored units. The following bow techs offer only a single bow weapon and are not too much better than the one before. The best bow you can get for trained units is in the Magic Tree and you don't need the other bow techs to get it. 

I have to conclude that bow weapons are not useful as they are outclassed by staves and do nothing but clink against anything as good as chain armor. Tarth has a few slightly better bows, ending with a wonderful late game bow that ignores 50% of armor. Other than that, you are better off with melee or staves. Ideally you should get axemen and then staves. Once fire mage group with two axemen groups is pretty much a free lease on clearing the lands of monsters. Bows never compete, unless you have zero resources and are desperate for some defense.

The AI usually inches forward one space at a time against ranged units making them really strong despite any initiative penalties. Also, I think the auto-resolve feature favors ranged units a little bit, just looking at Lady Irane auto-resolve some battles and not getting any scratches on turn 1.

I have been using a shortbow I picked up on a another champion. It is much weaker but useful for those governor heroes who are never going to be great at combat. I do agree that Champions should have bonuses to staves and bows compared to normal units, since the 3x bonus what makes it valuable for squads of units.

im a very fan of archer gameplay so i tested a lot this in past and actual beta

atm the situation is:

-champion archers are someway weak, but with a good amount of mana and some spells you can still kite and sometimes defeat monsters you couldnt defeat otherwise (Still having infinite mana you could do the same just with any caster )

-crit are way nerfed (but they were so OP so this is right) probably cause of this bugfix "Fixed an issue causing the +50% crit damage with Path of the Assassin to be per level" now crits are balanced imo" so full assassins dont really 1shot things anymore

-troop archers are definitely too strong now. 

thats not a archer problem but a general problem of troops having attack multiplier so whenver troops have high attack is just better to be ranged cause the opponent will reach you already weaken (or dead)

It would make more sense to have bows do less damage overall and have some ability to ignore armor. As long as they are doing 2-4 damage things can be balanced. If enemy units are not wearing armor until after I get bows, that is bad AI. There needs to be a use for bows, but also a solid counter. Mounted units are the natural counter so far, but you never see the AI use them. If I am Tarth, I can't hit a damn thing when the enemy uses Belt of Precognition and a Horse. The AI should learn to counter bows so that we can make bows more competitive.

I wanted to put ranged in perspective. Yes, it's a great tactic against the AI, but only so far as the AI is not equipped to deal with it yet.

I think bows should have more armor piercing (maybe 25/50/75%) and compensate with with reduced accuracy (-25). That would be more realistic and balanced I think. The initiative penalty should go down a bit as well.  

That sounds like an AI problem.

I think we need better and specific weapon promotions to replace the apprentice swordsman-style chains we have now.  The bonuses need to require using the proper weapon also.

yes you are totally right here

seems complicated though, i doubt we will ever have such a smart ai

maybe it should just create a "balanced party" similar to civilization, like a couple of ranged units couple of mounted and a couple of heavy armored melee or something