NP represents a nonlinear physiological response to hard work. If my FTP is 300W, riding at 400W is significantly more difficult than 200W. The physiological cost of that 400W effort is much more than double the 200W effort. TSS maintains that nonlinear response.
Worth noting that a lot of the mathematics here is just to get ballpark figures that make some sense and roughly correspond to what we think happens in the body. Coggan took power to the fourth order in the NP calculation because, meh, he thought it was a good fit. The following calculations like TSS and so on are similarly arbitrary.