Sometimes inside corners get coped, sometimes they don't. Usually, copes are used on trim work such as baseboards, crown moldings, chair rails. They don't get used on cabinet or furniture moldings. If the moldings have a complicated profile, lots of little shapes and transitions, it doesn't make sense to cope them.
If you are installing crown moldings in a room, the first piece can be cut with square ends and put in place. The next piece typically gets a cope on one end, a square cut on the other and this continues around the room until the last piece, which will usually need a cope on both ends. The pieces of molding are cut a little long, 1/16" or less, and sprung into place. This pushes the cope tight against the preceeding piece making for a tight fit. If both ends of the molding were cut with an inside 45, when you nail them, that joint in the corner will often be pushed open. When you have moldings that are too complex to reasonably cope, you often will use an inside miter cut that is slightly less than 45 so the faces meet tightly, then you avoid nailing right in the corner, which is a good idea with many corners, anyway. It's not like you need the corner nailed on a long piece of molding that is nailed every 16" along a long wall.
It's about appearance and practicality. Cutting a long piece of molding that goes from corner to corner in a room has to be cut exactly or the corners will show any difference, long or short. You may also have issues with corners not being exactly square and the molding not sitting at the exact correct angle. Coping only one end and leaving the other end square eliminates the need and difficulty in being absolutely precise, while giving the appearance of a perfect fit.
Cabinetry and furniture work is different. You seldom have to worry about a little difference in spring angle, out of square corners or a wavy surface that you attach the moldings to. Furniture makers are used to finer, more precise fitting and usually aren't working with long lengths, they have more control over conditions. The joints are also more readily seen and any slight roughness in the cut or fit isn't acceptable. You won't see copes used on professionally made furniture.
I install a lot of manufactured kitchen cabinetry. Crown and light rail moldings are often added. They are usually prefinished hardwood moldings and this is another situation where coping inside corners doesn't make much sense. It's just a lot easier to miter corners and get a great appearance rather than to cope. There can be a compromise with copes at the bottom of the moldings where it might come to a tiny point. This isn't an issue with a miter but with a cope, this point is often squared off. It's often very delicate and doesn't look quite right compared to a miter where the mating is continuous all the way.