You would fetch the data for a specific user by passing the UUID as a parameter. Just like you do it with a normal autoincrement ID.
As for transformers, they are used to keep the data consistent without breaking changes in the API. Also, another benefit is, changing the database field names to something completely different so people don't know your database structure and field names.
What I mean by that is, let's say you have a field called created_at in the database and for some reason, you want to change it to created_on using a migration. You would change it, make changes in the code to reflect the latest migrations but If you don't use a transformer, your end users (developers who use your API) will have a problem with data not showing up and all kinds of errors.
You can't do this with a Model's $hidden property.