Was Jim Morrison a poet? He certainly wanted to be seen that way, but does his work really deserve the name of poetry? That's a complicated question, because it raises the issue of whether song lyrics are poetry in the first place.
There are poetic traditions, usually oral traditions, in which poetry is always combined with music and never separate from it. Gaelic poetry, for instance, was written this way until the twentieth century, and sometimes still is. That isn't really the same thing as rock lyrics, though, because in poetic song traditions the melody is seen as a carrier for the words, a memory aid more than anything else. The music in these traditions is never seen as being equally important with the words and is never allowed to overpower the words. It is usually seen as being very untraditional to have more than the simplest instrumentation as an ornament to the song. A “good singer” is someone who sings the words clearly so they can be easily heard, and who expresses the emotions in the song- not someone with a powerful or note-perfect voice, and not someone who can deliver a charismatic performance.
Rock music is almost the complete opposite of this. The music is usually seen as being more important than the words, to the extent that it may not be easy to even hear the words. The singer's charisma and personality are on display- and never more so than with the Doors. So, while rock lyrics can sometimes be poetic, rock music is not a poetic song tradition. The lyrics are almost an after-thought in rock.
If rock music is different from poetic song traditions, then any assessment of Jim Morrison as a poet must depend on his words alone, without the benefit of his performance or the music. In other words, what would you think about Jim Morrison's work if you just saw the words in a book? Opinions on that question have been very mixed.