I read that a capacitive dropper supply, like those found in some LED light bulbs, has issues like inconsistent brightness, flickering, and voltage fluctuations.

Is the following correct?
The flicker isn't caused by the cap. Fluctuations on the secondary are due to all the following:
In other words, it's a non-regulated output.

Is the following correct?
The flicker isn't caused by the cap. Fluctuations on the secondary are due to all the following:
- fluctuations of the primary (mains)
- fluctuations in the load
- mains frequency
In other words, it's a non-regulated output.