1 hit point off a defender is not going to get them dead... like I said they kill knights with impunity.
But 1 hp less and then wait a turn means 0 HP less. And that is even worse.
so then you are saying bring 36 knights with the 12 Cats since the cats will likely not do anything. Just kill off knights to get those hit points down.
If you are going to use 36 knights and 12 Cats, you might as well use 39 knights and 0 cats. Artillery is only worth it in large numbers.
You can also build 12 knights and 96 cats. (24 knights is 24*70=1680 shields, and 1680/20=84 cats) or 24 knights and 54 cats.
And again I say... why bother with bombard? it is pretty much useless if you just have to sacrifice your units anyway.
at low difficulty levels, or when you are not playing AW. It is probably better to just build nothing but horseman/knights/cav.
Some points to note:
In vanilla, catapults are less useful than in C3C. They hit less often. But artillery from the industrial age is still good enough. So do try those when/if you reach the industrial age. But I remember using cats in vanilla too. And not unsuccessfully.
If you damage a defender, it will move to the back of the stack, and the next strongest defender will be at the top/
So if a stack has 20 vet units, and you remove 10 HP, then that means 10 units will have 3 hp and 10 will still have 4. If you want to red-line at least 1 unit from this stack, you'd have to remove at least 41 hp.
In any event, you should certainly not spend 20 turns damaging units in a single city, the city should be taken the very turn you attack at.