I see no issues with Raise Dead other than what the DM puts in the way (and the whole "willing" thing).
There are countless occasions where a King has had an Assassin, or many, on retainer. That is not public knowledge (normally). I see it no differently for a Cleric to be on staff either in secret or otherwise (if he worries about "publicity").
And if you are going to have a zoo with sentient creatures, then guess what, morals and publicity go out the window as you are dealing most likely with a totalitarian state - and what the King says is law - there is no worrying about who thinks what. After all, if the King is putting so much money and resources into such a zoo, then he has more than ample resources at his disposal to allow for the "reinstating" of life into exhibits of value. Consider it part of the maintenance costs.
I'd tend to think of such a set-up in the same way as how Caligula managed his empire. He did many outrageous things that the common folk loved. To them he was a fun and entertaining emperor. But, to the aristocracy, he was a living nightmare. Where that all goes is that he had power and money - he could do what he wanted. A King in this scenario is very similar here.
(And using that comparison, the King may be doing his thing, but the nobles could oppose it - and that could lead to a whole other dimension of the campaign.)
Overall, I think that the premise of such a campaign could be interesting. However, I also think that it could get old quickly. If all a party ever does is serve a single master as nothing more than acquirers of beast fodder, then it would eventually devolve into doing the same thing, time and time again. While the creatures may change, the overall effect would be the same - find creature, stuff in box. You will probably want to use this as additional quests, or main quests if they are not doing something else, but having a diverse sandbox will be very important to prevent burnout.
But too, it'll depend on the players. If they really get into it, then great. But I've too often see players who are a little hyper and easily distracted - so you will still want a range of things they'd be able to do.
Regardless, have fun!