For my two pennyworth, and as a senior observer in the Institute of Advanced Motorists, there are two types of engine breaking (someone will tell me there's more of course) 1. engine braking in the gear you were driving in and 2. engine braking by going down a gear(s) to force extra braking. For road use 1 is good 2 is bad. Here's the reasons. As has already been said, brakes are cheaper to replace than engines and transmissions, and these days they are much more efficient and reliable, negating the need to "save" them for when they are really needed. Engine braking naturally occurs when you lift off the throttle and can be used to slow the car before applying the brakes to stop. Modern cars can take very low speeds with the clutch engaged before labouring so if you plan the stop correctly you can almost stop under engine braking from a distance with little or no stress to any components. When driving down steep winding hills, however it is best to take a lower gear and use engine braking to keep the car in check to that the brakes can be used to assist when needed without the fear of overheating and fading. One of the things we do as advanced drivers is see how well you can drive in all traffic conditions without using the brakes but also without using excessive engine braking. It is amazing how much concentration and forward planning you need to do this, but the results are quite spectacular in respect of mpg, brake pad longevity and progress.
As for racing rules I am not a racing driver so cannot comment.