I see what you're saying but I don't think massed archery should be a threat to things like dragons, etc. I'm not sure what the solution is though...
I think the problem lies in removing cannons as a threat to monsters. IMO cannons *should* be a threat to monsters. The problem lies in the fact that it is so cheap and cannons are so reliable, that they become simple, inexpensive hard counters to the point that it becomes worthless to take monsters at all. The concept that a cannon is a counter to monsters is fine, they just need to not be such a cost effective hard counter.
In my mind what needs to happen is one of several possible options, all of which I think are acceptable and would allow for more play with monsters:
1) If cannons are to continue to be hard counters for monsters, they should be priced in the same range as monsters are (~ 200+ points) so that it's more of an even trade
2) reduce the effectiveness of cannons against things other than monsters/chariots (allow an initiative test to avoid cannon ball shots for infantry, or perhaps a ld test, or something like that; remove grapeshot, etc.) so that it becomes more of a gamble to take a cannon. If you take 3 cannons and your opponent doesn't show up with any monsters, those cannons should be wasted points. Right now cannons are cheap enough and versatile enough that even if no monsters/chariots/multi-wound models are present (the things cannons excel the most against) they can still churn out considerable damage with little in the way of mitigation.
3) reduce the accuracy of cannons. The artillery die mechanic is too easy to predict. Perhaps add a ballistic skill test before the shot, then modify the artillery die based on the success or failure of the ballistic skill test. (Perhaps roll 2 or 3 artillery die on a BS failure[include range penalties, cover, etc.] and allow the opponent to choose the result) Bolt throwers are a good example here. Due largely to the BS requirement of bolt throwers, they can do lots of damage to monsters, but are by no means as reliable as cannons. Bringing cannons more in line with bolt throwers could swing the balance around a bit more. (Maybe make the cannons STR 6 ignores armor, multi-wounds d3+1, thus reducing their instant kill potential)
4) there are probably others more viable than the ones I have suggested here...
My point is, making cannons not countering monsters doesn't fix anything, it just switches from having lots of artillery on the board in a fantasy game to lots of monsters on the board (which can also be a bad thing). Rather the degree to which artillery make monsters and such a non factor is what needs to be reduced.