What am I doing wrong ?

[Kekvit Irae]

Cannons suck in ETW. The volume of fire they can produce, and their accuracy, are both too poor to be worth their stack slot. In some very rare situations they can be effective, like guarding a sole breach in a fort wall through which the AI will funnel all their troops. But in the open they're pretty useless. I never us them. A unit of Line Infantry will always kill more than a unit of artillery (unless you get very lucky).

Two words: Canister shot.

I have written a haiku to show you how much I enjoy artillery during land battles:

I love canister,
It murders infantry guys.
Routed, shattered, dead.

[Zarky]

I like artillery. Once you get explosive shot and decent cannons enemy will be at routing point even before they meet your line infantry, not to mention that they'll be running away before their first shot if you get some cavalry on their rear.

[Ars Moriendi]

Thank for all the detailed answers guys.
It now seems I started this thread a bit prematurely, with only a few hours of game experience. Since then I've gone through some 40-50 turns, and many of the issues stated in the first post, well, I kinda learned to live with with them, or work around them.

Like this :

1. Hidden units - not much of an issue. They can (usually) be found quite quickly.
2. Chasing small armies - rationalized away as responding to guerilla and raiding warfare, which is supposed to be costly and time consuming.
3. Naval battles - it was me sucking - I've read some guides and they helped.
4. Artillery - buggy, but can't live without them (more below)
5.6. Houses & walls - turning elaborate masonry to dust- still pointless gameplay-wise, but hey...
7. City stealing - never happened again, so I guess it's ignorable.

About artillery being useful or not :

They generally don't kill much(*). However, they enable the rest of your army to do so - the AI feels compelled to leave its positions and attack you once they're out of arty and you still have some ball-hurling devices pointed at them. Needless to say, defensive battles are more cost effective than assaults. And then, there's the morale hit, as mentioned.

(*) Sometimes they do kill an insane amount of enemies - ever witnessed a scene where your dozen cannons unload, simultaneously, canister into the center of a densely packed blob of 4-5 enemy units ? Unholy carnage and instant mass-rout :).
I'm still somewhat disappointed by the lack of killing power for the carcass shot - after minutes of pounding at enemy positions, my howitzers only rake in 5-10 kills each, which is a bit underpowered, considering the impressive pyrotechnics display and rather scary noise they're making.

[Kekvit Irae]

I have to agree that carcass shot is pretty worthless, but explosive shot is totally worth it. A well placed shot can kill plenty of men in a tight formation.