In my personal opinion you should avoid composite primary keys due to several reasons:
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Future changes: when you design a database you sometimes miss what in the future will become important. A significant example for this is thinking a combination of two or more fields is unique (and thus can become a primary key), whereas in the future you want to allow NULLs or other non-unique values in them. Having a single primary key is a good solid solution against such changes.
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Uniformity: If every table has a unique numerical ID, and you also maintain some standard as to its name (e.g. “ID” or “tablename_id”), the code and SQL referring to it is clearer (in my opinion).
There are other reasons, but these are just a few.
The main question I would ask is why not use a separate primary key if you have a unique set of fields? What’s the cost? An additional integer index? That’s not too bad.
Hope that helps.