One of the reasons kakashi can only do chidori 4 times is because he is using the sharingan as a non uchiha. Uchihas are able to use the sharingan more effectively because it is meant for them. And since kakashi has no uchiha blood it takes up more chakra for him to use the sharingan. So since he can only do chidori with his sharingan, he is only able to do a significantly less amount of chidoris. Still 4 times is quite impressive. But this explains why sasuke is able to do it twice already, he is much more suited for sharingan