The twelve hour rule is a requirement (must) when one's parrot has become aggressive and/or other behavioral problems are presenting, and the goal is getting the parrot back from the edge.
Commonly, today's homes are near 24 hour active. And, that is where it becomes a problem. You need to monitor your home's active hours. And yes, TV 'ON' is part of the measurement, unless your using ear bugs and the cage cover is a true black-out cover.
Most homes are nearer to four hours of true sleep than someplace North of eight hours, let alone ten or twelve. According to most studies, us Humans are averaging less than six and a half hours of sleep. So, the average Human is sleep deprived. We tend to fall asleep while drive where our parrots only take large bits out of us.
Regarding the cage. Unless you have a cage body that has a depth greater than 26" it should roll though most doorways. Some cages have 'Seed Catchers' that are removable that will allow them roll though a doorway once removed.