I'm working on a bottom end Falcon, bringing it back from being single speeded.
I just put a Shimano cartridge BB in it and the left and right threads on the BB shell must be miss-aligned. If I tighten down both sides of the BB, the BB becomes stiff. You can see the BB sits slightly crooked when the main body of the BB is installed. I had to loosen the main body to get the sliding side in.
If I tighten the sliding side tight the BB binds pretty hard. If I leave it slightly loose, it's not bad but still a bit of drag.
I'm sure the BB is not cross threaded as I was able to thread both sides in by hand.
It's not that it needs facing as the problem is there before the main body is tightened all the way down.
Having it chased won't change the alignment of the threads.
I don't see any way around it other than leaving the sliding cup slightly loose - after all, it just supports the body.