I remember kakashi using primary lotus before (not sure if this was in the manga too or not, i can't remember).
But i believe that he CAN use gates, and here's why:
When kakashi learned that gai could use gates, he was surprised that he could do with through sheer force of will.
I believe that this means that it is possible to do by some other means. Now the primary lotus is suppose to require the first gate because of the immense toll it takes on the body. Meaning that if kakashi used it, he had to have used some gates perhaps. (I don't think kakashi's taijutsu prowess is greater than base lee (who needs to use the gate to perform the attack). So if kakashi performed the attack, i believe he knows the "other" method. This means that kakashi likely can use higher levels. I know kakashi doesn't have strength like lee who can use 6 gates, or like gai who can use 8. But perhaps he has a way that doesn't take as much of a toll on the body.
Also he has the sharingan, so he has seen gai perform the technique multiple times. If he has a way to do it without the need of "force of will", he might be able to achieve upper gates levels.
Now the question is "why doesn't he use it". I think its because 1) Lazy writing... kakashi has "1000 abilities" that he never uses because reasons. 2) Maybe he knows a way to do it without needing the amazing force of will, but maybe it still wrecks his body after. he doesn't have gai's stamina and it would leave him useless.
But i believe that he CAN use gates, and here's why:
When kakashi learned that gai could use gates, he was surprised that he could do with through sheer force of will.
I believe that this means that it is possible to do by some other means. Now the primary lotus is suppose to require the first gate because of the immense toll it takes on the body. Meaning that if kakashi used it, he had to have used some gates perhaps. (I don't think kakashi's taijutsu prowess is greater than base lee (who needs to use the gate to perform the attack). So if kakashi performed the attack, i believe he knows the "other" method. This means that kakashi likely can use higher levels. I know kakashi doesn't have strength like lee who can use 6 gates, or like gai who can use 8. But perhaps he has a way that doesn't take as much of a toll on the body.
Also he has the sharingan, so he has seen gai perform the technique multiple times. If he has a way to do it without the need of "force of will", he might be able to achieve upper gates levels.
Now the question is "why doesn't he use it". I think its because 1) Lazy writing... kakashi has "1000 abilities" that he never uses because reasons. 2) Maybe he knows a way to do it without needing the amazing force of will, but maybe it still wrecks his body after. he doesn't have gai's stamina and it would leave him useless.