Interesting. Multibounce. A way to duck sweepers, remove counters etc. Seems a bit costly to use; but maybe being able to sweep everything up on the cheap is too powerful.

I note the 'other' to prevent shennaigans with exiling itself. And nothing bad seems to happen if you use one on another one. So.. nifty.

Works very similarly to Safe Haven and Synod Sanctum. This is perhaps a bit more expensive than it needs to be by comparison with those. It also probably doesn't need to be rare.

Templating-wise, you could probably mirror Banisher Priest with this: "Exile another target permanent you control until ~ leaves the battlefield."

this was created to be safer than Safe Haven and Synod Sanctum, which both involve a decent sized risk of backfiring due to meddling opponents

while it's true Banisher Priest works exactly the same, this wording makes it clearer that if the box is blown up with the blink ability on the stack the target will still return safely and not get trapped

Odd interaction with two of these on the board. They can target each other in response to their own abilities. Probably not broken, though, since the second safe deposit box is still kind of redundant. That, and the cost to activate to exile a Nekrataal, then activate a box, then activate a box... yeah... ": Exile, then return target creature to the battlefield" seems like a fair activation cost.

Given Mistmeadow Witch, yeah.