Well, I'm still reading the manga, but moreover, I can say that there are some reasons behind all this. If I'm wrong, feel free to correct me as I'm still reading the manga.
If you have only viewed the anime:
You can see how the scouts wasted their time by identifying if there is any breach in the wall. They were all confused about the appearance of the Titans from nowhere and they were under the false impression that people have evacuated safely from the village without any harm.
If you don't mind spoilers, these are the reasons he might have done so, as per manga:
I'll explain the drawbacks you mentioned above:
- He risked losing Reiner/Berthold powers if they would be eaten by titans
Since the titans were made from the spinal fluid from Zeke, they will always listen to the beast titan/Zeke. So they will not eat Reiner and Bertholdt unless Zeke says so. And why would he do that, because all three are there for the only one reason to get back the founding titan.
- He wouldn't confirm that way if Eren's titan is the one they are looking for
The main goal to invade the Paradis Island was to get back the founding titan (Eren is the current holder), so basically they were kidnapping Eren, even if you feel Zeke's action doesn't comply with the goal, he might have done that to misguide the scouts.
- He leaked important information to Recon Squad that Titans are transformed people (Hange figured it out)
He wanted them to know what is actually happening outside the walls (Especially about the war). As the Fritz king bloodline falsely spread the rumours that there is no humanity outside the walls. So basically he wanted to let them know, that you've been told wrong about everything. Later in the manga Zeke, reveals his true colours and agrees to help Paradis Island to defeat Marley so that New Eldia can be built.
The last sentence from above might not be correct, because Hanje suspects that Zeke is brainwashing Eren and have different plans, acting as a double agent, because Eren turned against Military. Later he also turns Levi's subordinates into Titans (As they drank wine with Zeke's spinal fluid which was imported from Marley), so his goal was to kill Levi in this, as he thinks Levi will not fight his comrades (after converting them to Titan), which he later realises that he was wrong after getting captured by Levi again.