DrJambo
Crash-test dummy
I agree with a lot of points here, and from both sides. 
As they stand, catapults and cannons are relatively poor compared to their more mobile non-artillery units of the same period.
Furthermore i think the movement of 3 for Cavalry is completely absurd and totally unbalancing. The first change i made was to reduce this to 2 and this makes for a much more enjoyable game. A movement of 3 just allows them to do too much on their go... i.e. reach a far flung enemy city, move-pillage-move to safety, faster than tanks! Once this is implemented the game plays fairer
I have tried many adjustments to try and reach a happy medium between the 2 following the reduction to cavalry movement:
1. First i tried catapults and cannons with a rate of fire of 2. THis was a good addition but i found it to be a little on the powerful side, especially considering that the AI doesn't use them as much as humans or in as big stacks. You see, artillery really becomes useful when they are used in large stacks, where 10 cannons can reduce an attacking army to rubble before it has even launched one single assault. THe AI, since 1.17 always seeems to use one artillery supported by a defending unit (not so effective).
2. Then i hit the jackpot. Instead i made all artillery have a range of 2. This means that catapults and cannons can be used more effectively as with their poor movement they now only need to get to within 2 squares of a city. They can also have more assaults on approaching enemy with the increased range.
In terms of getting the AI to build more artillery, just flag that option under the Civilisations tab in the editor. There you can chose what types of units the AI will prefer to build such as navy, airforce and artillery... you'll notice that currently no AI have the artillery option flagged and little have either navy or airforce. Most of them have only offensive units flagged. I have artillery ticked for the majority of AI civs and they now build as many as me
Another interesting feature is if you give archers/longbowmen/bowmen a zero range bombard ability similar in value to their offensive stat. This means they get a free shot at an attacker similar to the way artillery do as long as they are stacked with others, but without being able to use bombard offensively. It works very well and makes the archer set worthwhile to build..
One advantage you forgot to mention with artillery is that when you build artiillery they are there to stay as they cannot be destroyed unless sunk.. Therefore, if you lose them, you can always regain them later, thus not losing money. When cavalry lose...they die
Cavalry to movement of 2 is essential tho...

As they stand, catapults and cannons are relatively poor compared to their more mobile non-artillery units of the same period.
Furthermore i think the movement of 3 for Cavalry is completely absurd and totally unbalancing. The first change i made was to reduce this to 2 and this makes for a much more enjoyable game. A movement of 3 just allows them to do too much on their go... i.e. reach a far flung enemy city, move-pillage-move to safety, faster than tanks! Once this is implemented the game plays fairer

I have tried many adjustments to try and reach a happy medium between the 2 following the reduction to cavalry movement:
1. First i tried catapults and cannons with a rate of fire of 2. THis was a good addition but i found it to be a little on the powerful side, especially considering that the AI doesn't use them as much as humans or in as big stacks. You see, artillery really becomes useful when they are used in large stacks, where 10 cannons can reduce an attacking army to rubble before it has even launched one single assault. THe AI, since 1.17 always seeems to use one artillery supported by a defending unit (not so effective).
2. Then i hit the jackpot. Instead i made all artillery have a range of 2. This means that catapults and cannons can be used more effectively as with their poor movement they now only need to get to within 2 squares of a city. They can also have more assaults on approaching enemy with the increased range.
In terms of getting the AI to build more artillery, just flag that option under the Civilisations tab in the editor. There you can chose what types of units the AI will prefer to build such as navy, airforce and artillery... you'll notice that currently no AI have the artillery option flagged and little have either navy or airforce. Most of them have only offensive units flagged. I have artillery ticked for the majority of AI civs and they now build as many as me

Another interesting feature is if you give archers/longbowmen/bowmen a zero range bombard ability similar in value to their offensive stat. This means they get a free shot at an attacker similar to the way artillery do as long as they are stacked with others, but without being able to use bombard offensively. It works very well and makes the archer set worthwhile to build..
One advantage you forgot to mention with artillery is that when you build artiillery they are there to stay as they cannot be destroyed unless sunk.. Therefore, if you lose them, you can always regain them later, thus not losing money. When cavalry lose...they die

Cavalry to movement of 2 is essential tho...