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Even in a single Castle, you get +7 hippogryphs each week, and after 20 weeks, you'll have a stack of 150, which is already a significant force. They'll be among the top damage dealers in your army. And yes, I mixed it up – that's the weekly monster.
A monthly monster, on the other hand, is a different story. If you want, you can create such a combo that you won't have any problems with your army; you just need to find the resources. I've looked into it, and it's not available for all factions, but the hippogryph is the best choice here. Of course, you'll have to fight without them. If you don't buy hippogryphs for three months and catch a monthly batch each month, you'll accumulate 10,000 hippogryphs. In short, it's overpowered and can't be countered.
In HD+, both weekly and monthly monsters are disabled, so it all depends on a gentleman's agreement – whether or not to use them. But again, this is only relevant for speedruns; it's not necessary for completing the game.