If we are dreaming, Why not apply hardness/strength ratings to other things as well as walls ?
There are already material properties related to shear strength, etc. Simply add limits to each creature indicating what shear forces they are capable of providing, or better yet, a translator that indicates what strength value = which material force value. Then, we have a generic solution, which permits us to predict what creatures can batter down or rend walls, weapons, statues, or really any item.
It has always bothered me that wooden cages can capture dragons , ogres, and giants. Now, If I had to construct giant cages out of steel or adamantine, that might be a different story ....
Re: cooldown - I think something like this is necessary. Alternatively, if we are modeling strength vs. material durability, as above, the unit of definition could be something like "10 strength = able to rend a 10,000 strong wall in 5 seconds' (or whatever - Im not sure the units for shear strength in materials). Maybe there could be a multiplier for size, too, so larger creatures would appear stronger and smaller creatures would be weaker. That way, creatures have built in cooldowns, which are proportional to strength. Dragons could tear through weaker (and indeed, most) materials rapidly, while maybe even weak, smaller creatures could make it through moderately durable materials....if you have them a lot of time.
Anyway, just thinking out loud here...