I was contemplating posting this in bugs vs suggestions... anyway.
Once a cave front gets a door built on it, no light enter the cave, even if the door is open.
This is partially mitigated by Building | Wooden | Ceiling & Floor which illuminates the interior.
So my suggestion would be to allow an open door &/ shutter to let light in the cave. Say 5-6 tiles 10-12m
AND
Do not auto illuminate the depths of the cave even with built ceiling&floor.