Khan had to come back and haunt Kirk in some manner.
One thing I find that never made sense in TWOK: Chekov was never on screen but Khan knew him (which I can accept, after all there were 430-ish people onboard and we didn't see all of them), so Chekov would know where the Enterprise
left him at. Surely when surveying planets for Genesis, he'd remember: Didn't we leave an evil super-human stranded on a planet in the Ceti Alpha system--and isn't it missing a planet?
Commander Austin Harris, First Officer, Deep Space Nine (by FltCpt. Bossco)
8.01 - Darkest Before Dawn
(Chapter 8 added, 12/09/2015)