I know what you mean regardling things like kill with x, and for a game like that if each player is given a different kill with creature then you may well want to keep it hidden.
On the other hand, if you giving all players the same kill with creature then it could also work to let every player see that it is the same for all of them.
Not seeing the creature adds suspense, seeing what it is alters tactics.
I think it can more the case to have an open system with mana collect if each player/team has the same objective. I.e. There's 5 sprites on the map, and each player or team is tasked with retrieving 3 of them. I think in that case it's better to see each other's objective.
I think where you may be more likely to want objectives to be hidden is where player A has 'kill player B', and player B has 'kill player C' and so on.
I think you'd also be more likely to want hidden objectives if they vary for different players. I.e. Player A has 'kill with Elf' and player B has 'Collect 3 sprites.'
The Guild of the Cephalopods is now recruiting -
We embrace all.
- Chief Tentacle Arranger in The Guild of the Cephalopods.