Ok, we seem to have some trouble communicating with each other
Barrage and Precision don't give bonuses against cities, never. I'm actually dealing 2-3 damage per attack with a GG by the side, 3-4 with siege. But 3 longbowmen with logistics deal around 12 dmg per turn to a city, while not suffering counterattacks, which means that you've made the city's hp drop to 1 in 3 turns tops (counting the turn where you approach the city, and thus only get one attack against it), and then you just have to take it with a melee unit.
The corresponding siege unit is trebuchets (cannons come way later); they have way less chances to attack enemy units for xp, because of their shorter range, and the need to position themselves before attacking; more often than not, you will have to keep your distance against units for fear of the counter-attack. That leaves only cities to get xp, or garrison them in your own cities, while getting attacked (which isn't something you should be looking forward to, since you lose a lot of productivity if it lasts too long). Your siege units will take longer to get heavily promoted, and less of them will (usually one or two). And before they do, they won't deal that much more damage against a city, at most 3 times more than a regular longbowmen shot, and that isn't enough to justify their cumbersomeness (unless you don't have a UU in medieval/early renaissance).
By the way, I'm not geared towards war. I actually finished liberty, then went commerce, for Role-Playing purposes. You will get even better results getting into honour after dipping into liberty, but I didn't want to. My first war was a defensive war, Askia was a complete douche to me, and though that my military was puny (which it was, but he didn't though about the tactical advantage I had because of terrain); that war lasted a while, and got me some nice xp, but it wasn't until I left Askia with one city only, and I DoWed Bluetooth that my archers-now-upgraded-to-longbowmen started getting logistics, and killed everything.
My army was composed of two longswordmen, three longbowmen, and four SotL that cleared the beach for my landing (Harald was across a narrow sea).In Harald's defense I have to say that he didn't have iron, but Suleiman (the next one in the list) did, and he had just started building janissaries when I got there, so he was strong, but couldn't do a thing against an army
one era old.
And well, now that I own 2/3 of the capitals, nearly everybody hates me (except good old Gengis), but it took a while for everybody to understand my goals (3 DoWs, and 6 conquered cities, 3 of them capitals), so as long as you meet people somewhat far away from you, your good for trading.
You do have two good points:
-longbowmen are nearly useless once upgraded to riflemen; the only promotions they keep are siege and logistics (which is as good as blitz until mobile infantry, don't forget it).
-once you get to artillery, it is best if you have heavily promoted cannons than heavily promoted longbowmen.
And by the way, artillery IS a gamebreaking unit; extra range, indirect fire to use it (the big flaw of longbowmen, if any), and ranged strength to kill things, artillery has everything you want; there's no way I'm going to argue against its raw power, that can't be compared to anything before it. And with extra range and logistics, artillery is a God of War.
But if you want a Domination victory, you have to start way before dinamite, and longbowmen will help you push through all resistance. Catapults, trebuchets and cannons won't, unless you are forced to use them (just watch some Deity LPs, and you'll notice how rarely they are built).
You should try a more aggressive game with England, starting with an early war (preferably on your own land, to train your archers safely), beeline machinery, and go kick some ass with your promoted longbowmen (or your horde of ~6 longbowmen, if that fails). You don't even need honour, but you can take it if you want.
