Too much NBT data crashes game on multiplayer

So I was being an idiot and realized I can put NBT chests inside of NBT chests. (I think you know where this is going.) So, because this surly could not be a stupid idea, I decided to try it in a freeop server. I expected lag, but what I got was a Java error saying the NBT tag was 1 byte too long.

(as of writing) I could not rejoin that server.

Reproduction:
1. Go on a multiplayer server.
2. Place a chest, and fill it with whatever.
3. Control/Command + Middle click the chest.
4. Place another chest (not the nbt one) and fill it with stacks of the NBT chest.
5. Ctrl/Cmd Middle click the chest full of chests.
6. Rinse and repeat until you can no longer join and get the error that NBT data is too much to handle.
This could be fixed by predetermining how much NBT data middle clicking would take up, then not allowing you to if it is greater then the maximum.
-MurphyMinecraft