Painters secret, purposely withheld.
Several reasons. One is that the tape would have to go on the ceiling, often the walls are knockdown and ceilings are popcorn. The tape would pull material off the ceiling.
Second, it's tricky getting two coats of paint on the tape and then pull it without peeling the paint off the wall. Normally, you would use a razor blade, but at the ceiling/wall corner, it will leave a black line.
And finally, on textured corners like that, it's better to freehand a straight line by eye. Slick mentioned the lumpiness of texture, and using tape will get a straight line, but it won't look straight because of the lumpiness. Without seeing the work, it's hard to recommend or discount this method. If you do use the tape method, the tape has to be pressed firmly, 100% around all the little lumps and bumps. Paint the ceiling color on the wall and then the wall color right away, then pulled right away.
I assume you mean to remove the tape after everything has dried? Can you do that without the paint chipping into pieces?
Yes, some of the paint would be dry (the base coat would have to be to put the top coat on) but apparently it works. I guess the caution is it only works where tape would normally work (ie. if you wouldn't normally put it on popcorn, you wouldn't to use this idea either) and with tape that can be left on for at least a day without problems. I've never had an issue with pulling tape (I use green tape) but if it's been on there a while I use a razor to score the edge first anyway.
Another option I have tried and like a lot is a cone shaped brush. I got one last year because basically I hate taping and wanted to find a faster way to paint the edges without tape (and all the other gizmos leave me swearing). My chiselled brushes work great but I still mess up sometimes. Anyway the cone shaped ones are pretty reliable once you get the feel of them going.