I came across this report years ago. Not all incense is the same, and this part here should not be overlooked:
"However, several conflicting reports have also been documented. The effect of incense smoke on health and the mechanism behind it needs to be further studied in an animal model. To obtain further conclusive results, more epidemiological studies with better controls and a longer time period are needed."
Obviously, incense with synthetic fragrances are more suspect than those without. And you can tell the difference when you breathe it, too. I've largely switched away from cheap, bamboo core, synthetic incense for precisely that reason. This early report doesn't really discern between synthetic and non-synthetic fragrance, or incense with and without bamboo cores, or really much of anything. There's no such thing as a zero risk scenario, but this particular report doesn't say anything about what the LD50 is - probably why it states further studies are needed as that critical information simply isn't available at the time of its writing.
Have anything newer and better and more conclusive? Something that has a proper risk analysis attached to it?
To add, no, obviously it shouldn't be banned - we don't ban smoking. We regulate it. And I sure as hell would like to see more disclosure from fragrance companies in general, whether incense, home "air fresheners" or perfumes. Some of that synthetic stuff smells sick.