They haven't, you just think they have. There are real ways to gain such insight, but not through breaking your brain's pattern recognition capabilities.
> They've also helped me to manage my anxiety and depression.
Well, they are drugs.
> You can tell me that's an illusion, but you'd be mistaken.
What is an illusion and what isn't? I'm not saying you aren't having those experiences, I'm just saying that they are not actually related to some biological element of yourself, such as you living a human life. Psychedelics breaks our pattern recognition, sense data starts to get interpreted in different ways and we see, hear, and feel sense data in a different way. They just fuzz up the control system of your brain. While it's true that your normal experiences are not somehow "less illusory" than those drug experiences, it is true that they are a more accurate model of external reality.
Your mind is constantly refreshing its own model of reality, according to received inputs. Psychedelics totally mess up your model of reality. The problem is that now you are attaching to this messed up model of reality as somehow real and insightful. It's not, it's just what happens when your brain isn't functioning properly.