TLDR: Kakashi's inability to pass through things was mainly as a result of the bloodline limit restrictions of the Sharingan. This made the Sharingan use up a lot of his Chakra which limited the daily usage and time duration in which Kakashi could use the Sharingan. Hence effectively preventing him from utilizing its true capabilities.
Like Fumikage Tokoyami already mentioned, the Sharingan is a Kekkai Genkai exclusive to the Uchiha and so compared to Obito who could freely use the Sharingan, Kakashi's use was fairly restricted. An interesting encounter where this was mentioned could be seen in Kakashi's battle against Itachi.
This "incompatibility" basically ensures that non-Uchihas are unable to truly unlock the hidden abilities of the Sharingan and hence acts as an impenetrable ceiling cap for anyone who isn't Uchiha.
Now back to the question, Obito's "pass through" ability is a pretty advanced application of the Kamui which seems to require less Chakra as its only shifts specific sections of his body to the Kamui dimesion. Nevertheless, the precision, accuracy and timing involved would require a great deal of training and understanding of Kamui that Kakashi could never attain given his limited access to the Sharingan.