The word 'psychedelic' is not really well-defined. In its original context of describing the effects of LSD and mescaline, it was a little poetic, vague, and more catchy than actually useful, and in the context of just being a label for drugs that work with the same mechanism of action as LSD and mescaline, it's essentially just an arbitrary label.
Can cannabis actually be useful like the classical psychedelic drugs, I think is the question? In my experience and opinion, absolutely yes. I actually believe that Δ9-THC is one of the most powerful and profound teachers, given the respect it deserves. It also has a handy bonus of being essentially like two different trips in one because of how different the effects are between a route of administration that bypasses first-pass metabolism (like inhalation) and one that doesn't (like oral).
As with most powerful drugs, I feel that Δ9-THC is not easily defined. However, if I use it with the right set and setting and am willing to accept and give into the effects that it has in store for me, I do find it to be both extremely useful and extremely memorable. This is, of course, modulated by the way it is used. With low dosages of smoked cannabis such as taking a few hits off of a small pipe, I find it mostly comparable to drugs like 2C-C, 2C-B, and 2C-I, where the visual effects are mostly flashy and simple and the headspace is a little confusing but mostly fun. With high dosages of smoked cannabis such as taking big hits off a bong, I find the effects to shift into a different plateau of experience and become more similar to the likes of 2C-E, psilocin, methoxetamine, and salvinorin A. When taken orally in the dosages I have experimented with so far, I find it to be more similar to the likes of LSD, ETH-LAD, and diphenhydramine.
Yesterday I had an extremely powerful trip from taking three (I think) bong hits in the morning before taking a long, hot shower, and I've been thinking about this thread ever since. Δ9-THC requires me to give into its effects in a way that other similarly powerful molecules I've experienced do not, and in a way that I suspect would probably be difficult for a lot of people, and I imagine is probably why a lot of people stop using it due to problems like paranoia at least as they often claim. It's rare that I am broken down in the way that a powerful cannabis trip will do to me. By the end, I was crying in a completely full and relieving way that was both blissful in its release and terrifying in the mind trip that pushed me to that point and mind-blowing in the way that it all played out. For many hours afterwards I simply enjoyed a psychedelic-like afterglow of reflection and appreciation of the profundity, permeated with a sort of satisfied sadness, which I find notably distinct from how the afterglow of a lower dosage sometimes makes me feel happy but unsatisfied.
I haven't yet experienced something as profound from oral Δ9-THC, but I'm working with it. So far, I find it much better for experiencing vivid hallucinations that are as if seen with the eyes rather than the mind's eye, the latter being mostly what smoked cannabis tends to do for me. Edibles are fun but I definitely feel like there is something big waiting around the corner from where I have pushed them to so far. I have little doubt that I'm going to consider them a special and useful tool for a long time to come.
So, is cannabis a psychedelic? I have no problems considering it to be a useful drug alongside the other classical psychedelics, personally. In fact, I have many times considered that it may actually be my favorite trip in some ways, providing visuals, visions, and mind trips that can exceed those produced by many other substances under the right circumstances, although also providing lighter and more recreational experiences more easily than other substances too. Still, as with all drugs, I think what anyone specifically gets out of it will be congruent to what they need and are ready to get out of drugs in general. I wouldn't continue to use it if I did not think it was useful to me, but I am glad that it is.
I think that about sums up my thoughts on the matter.