A mixer allows diversity...routing signals to different locations..As in everything, some mixers are limited, and some can do a multitude of jobs...

Keyboards for the most part will serve without a mixer, though some if not most are very basic..

I have two very decent keyboards that literally do not need a mixer at all..
Roland G70 allows mixing of all keyboard parts, aux in mixing with its own effects, mic and harmony controls with it's own effects...and global eq and master effects, too.

My other , Mediastation, goes beyond the G70..it does all the mixing jobs of the G70 plus adds , audio monitors outs (pair), and a pair of cue outs, for separate feeds to house etc, besides the mains..It also has video outs..All with individual controls..