Do US electrical codes require ceiling electric boxes?
There is no specific requirement for light placement, although there is a requirement that there be some light in a room on a switch. This is sometimes accomplished by having no ceiling light, but having a switched outlet that controls floor or table lamps.

While you do not have to keep the fixture, you cannot remove the box if you leave a live wire in the ceiling. Also, the box must be readily accessible. 

One solution is to cover the box with a blank or decorative plate. On the ceiling you could mount a rosette to a blank cover and attach that (so long as you can easily remove it with screws or other means of detachment).

You say the power is disconnected, but it is not clear if that is at the ceiling fixture or further down the line. If you can find the other end of the cable that powers the fixture, you can disconnect it there. Then you can remove the box and leave the dead (disconnected on both ends) cable in the ceiling. I would cap and tape the ends for safety.  You never know when someone might decide to reconnect a wire.