Correct me if this is a misunderstanding, but wouldn't allowing Emoji inside passwords make them more secure? I assume that would make brute force attacks dramatically more difficult while also making passwords somewhat more memorable.
On the user side: the ability to remember them and accurately enter them across different devices. This is much harder if you consider not using a password manager.
On the server side: The database needs to be able to handle storing them. Projects I've worked on using MySQL5.6 can't handle emojis but others using MySQL5.7 work with them just fine.