Why is a steady cadence so important? Or is it?
This is really a pretty complex question. Without knowing where you read about "steady cadence being a good thing" or what the author meant it is hard to evaluate this statement, but this SE.bicycles answer presents data showing that riders don't ride at a steady cadence. Rather, they alter their cadence according to conditions of the ride, the level of power they wish to put out, and the choice of gearing they have available. So your initial premise may not be correct.

That said, assuming you are on a constant gradient, with consistent wind, trying to go as fast as possible over a fixed distance, then you want power to be constant, because constant power application is the fastest way from point A to B in those conditions. If power is constant, then cadence will also be constant, unless you are shifting. Most humans can maintain the same power over a fairly wide variety of cadence, even if it doesn't feel as good. Usually it is fine to self select what cadence you want. It may be the case that you prefer a different cadence when climbing vs on the flats. If that is so, do not feel that you have to shift to keep cadence the same as the terrain changes.

The second part of your question presents a scenario of alternate pedaling and coasting, and posits that since it may be more economical for automobiles to do so perhaps it will be so for human powered cycling as well. However, humans are not like internal combustion engines -- we have two different metabolic pathways to generate power, which are colloquially called "aerobic" and "anaerobic." Aerobic metabolic production of ATP via the Krebs cycle is relatively efficient, but when we need to produce power that exceeds our aerobic capacity we switch to "anaerobic" production that is sustainable for far shorter periods of time. Compounding this "supply of power" issue is the "demand for power". The demand equations for cycling power are well understood if not well known, but the aerodynamic component of drag varies with the square of airspeed so the power demanded varies roughly with the cube of speed in calm conditions. These two physical constraints mean both that cycling faster and then coasting requires more energy than cycling steadily at the average pace, and also that speeding up is more physiologically taxing. That is, 1 minute of high power followed by 1 minute of recovery is still more taxing than 2 minutes at the average power, even though the total joules of work performed is the same. This is the basis for why "high-intensity" interval workouts lasting X minutes can have a greater training effect but be much less enjoyable than the same X minutes steadily spent at the average power. 

As it happens, here is a plot based on data from a segment of a ride where the rider alternately pedaled and then coasted. This segment of the ride was done on a flat road, with almost no wind. The upper panel shows cadence; the middle panel shows speed; and the bottom panel shows power. 



The "sawtooth" in cadence and power are apparent, and you can see speed increase and then slowly decrease. For this roughly 4 km long segment using this particular pattern of pedaling and coasting, power averaged 100 watts. If, on the other hand, the rider had covered this same flat 4 km long segment at constant speed so that the distance and total elapsed time were the same, the power would only have needed to have been 70 watts, a savings of 30%. 

In this case, the bicycle used was a geared bike, so had the rider changed gearing he could have produced the required 70 watts with many different combinations of cadence and pedal force. In other words, steady cadence need not have been used. This is an illustration that cadence isn't terribly consequential, and you have wide latitude to ride at whatever cadence you want to meet the purposes you wish to achieve. If you enjoy pedaling and coasting, there nothing wrong with that.