Read above!- Let me explain firstly the reason why Minato warned Kakashi not to use Chidori and stated it was incomplete is because it is a close combat stabbing technique that required the user to run at their target at blazing fast speeds. So fast in fact that they could not react in time to deal with an enemy counter attack.
That is without a Sharingan as one of the benefits of having a Sharingan is the ability to predict motion so that is what made Chidori complete. His ability to predict and maneuver past any counter measures with his Sharingan.
- The reason why Kakashi does not use the Rasengan is fairly obvious it is because basic Rasengan can damage but is not an instant killing technique. Its a jutsu thats destructive power is based on the amount of Stamina ie Chakra one pumps into it and Kakashi lacks stamina. No one has ever been killed from a basic Rasengan take a good look.
Naruto - Rasengan's Kabuto he lives Kabuto has a rapid healing technique that countered it.
Minato - Rasengan's Madara he lives 1) That's not Madara, 2) thats a fake body..
Konohamru - Rasengan's Pains Hell Realm He walks away Umm no the fuck he didn't
This is partly why Naruto spent much time during the time skip developing his Oodama Rasengan as that has enough chakra to make it a killing Technique. This is why Kakashi says Rasengan is incomplete as the addition of elemental energy it becomes a true finishing move it was intended to be.