I could see that working out nicely, kinda like in Goblet of Fire where half the challenge was finding out what the next event was and preparing for it. Stuff like the gillyweed and Krum's shark Animagus form for the lake event were a fairly big inspiration for what I was thinking of.
To be fair that's the thing I definitely would want to avoid. "Having to figure out the event". Not just because that's unfair. But also because of how volatile it makes the whole thing. Just imagine what would that lake even be if one of the players didn't prepare a "breathing underwater magic"?! What if no one did??!! What if none of them opened the egg and was like "what are we supposed to do here in front of this lake?"
That would be a very awkward day.