1. Swimming flat makes breathing tough: Your body wants to float in a flat position. That's how your lungs are set-up and you have the best displacement and buoyancy in this position. Too bad you can't really breathe efficiently here! (unless you lift your head, but then you sink)
4. Shoulder impingment: And finally, as in the first photo above, swimming flat prevents you from having a relaxed shoulder during the recovery phase over the water.
Yep, an inefficient flutter kick is really hard work, but an efficient kick is not. If you tend to get leg cramps when you swim or feel extremely out of breath after a 50m swim, that's a likely sign that you're using the wrong muscles to kick and no doubt that is proving to be a big deterrent to more kicking.
I really, really hate using a kickboard, though. Do I have to?
Kicking with a kickboard is really challenging. It is a great conditioning tool, and that's why a lot of competitive swimmers use one. But they generally already have a high level of kicking skill to start with or the luxury of many years in a swim club to gradually develop it as kids.