Traditionally I have always used an ID column in SQL (mostly mysql and postgresql).
However I am wondering if it is really necessary if the rest of the columns in ea
Don't confuse the logical model with the implementation.
The logical model shows a candidate key (all columns) which could makes your primary key.
Great. However...
In practice, having a multi column primary key has downsides: it's wide, not good when clustered etc. There is plenty of information out there and in the "related" questions list on the right
So, you'd typically
The main exception is link or many-to-many tables that link 2 ID columns: a surrogate isn't needed (unless you have a braindead ORM)
Edit, a link: "What should I choose for my primary key?"
Edit2
For many-many tables: SQL: Do you need an auto-incremental primary key for Many-Many tables?