Quoting hadith sources

I believe we have to assume positively that everyone or at least someone in the audience will want to check our sources. 

Quoting the sources is a good practise.  Never mind if they actually check it or don't check it - we don't need to deprive them of the information.

This will help to train people to identify and be alert about hearing hadith without sources .  It assures people that what they hear is from somewhere legitimate - not just from hearsay.  This is a problem now. Because people are so used to hearing hadiths without the source being quoted, they easily believe and forward or relate what they hear or read to others without any concern for the validity of the hadith.

Quoting the source also helps us greatly in ensuring that we quote hadith from which the source is known to us, and/or trusted.

And Allah knows our intentions best.