I'm not sure why various items trigger each other's cooldowns, probably to prevent players from roflpwning bosses in seconds with just a few items.
Although, only the Larcenies deal direct damage. The other items are more effective at clearing out packs of mobs, which isn't as useful on bosses (except for Worm and, to a lesser degree, Cursed Arthas). And since buying items is a perfectly cromulent use of the player's gold and lumber, I don't think there should be any reason why different item types trigger each other's cooldowns. If the player was skilled enough to buy multiple item types, then he should be rewarded with the ability to use all those items.