My take: While it's very tempting to concern ones self with ground distance, it's irrelevant. Aeroplanes fly in air, not ground! It's all about frames of reference.
Consider your track through the body of air in which you fly. If you just pick a heading and go, it's a straight line.Conveniently the body moves left and right sufficiently to put you back where you need to be at the end of the line.
If you crab and fly the magenta line, your groundspeed decreases, you fly a longer, squiggly path with reference to the body of air (which is the bit that matters).