IMO, the reason a cover letter would have contact details is because it is a formal letter and therefore set out as a business letter, with your contact details as well as the recipients. If you're applying for a position where writing up letters is included, it demonstrates your ability to set out a formal letter too. It's often pulled apart from the main resume, so an address helps it get back there.

A cover letter is supposed to be personal to the position you're applying for, so should refer to the name of the company, position you're applying for, contact's name (if known), and how you found out about the position. It should add to/enhance what's already in your CV, so as you say, you don't want to say the same stuff over again. It might also include relevant stuff like your (in)ability to work outside regular hours, licence and car and those informal skills that would make you suitable for the position (eg how being a parent has honed your time management and organisational skills). It's a good idea to close with something about being available for an interview, so having your contact details there on the cover letter saves the reader from searching through your resume for them.

At DH's old work, they'd immediately throw any resumes that had poor spelling and grammar or had generic (or no) cover letters. People would often get through for an interview without anyone reading their resume, so it's important to make a good first impression.

Ok, more than what you asked for, so I'll run away now...