In perhaps a larger sense, runners train to make the most of the abilities they have been given. This desire to excel dwells within some before they ever begin to train (or often before they begin to run!) and others find that passion along the way, having been "bitten by the running bug," so to speak. Competition serves as a catalyst, raising the bar higher (metaphorically in running, literally in vertical jumps), and assists in the achievement of those personal goals. Realize that this refers to competition in fair spirit and in fair play. Cheating with drug use or other means adulterates the purpose of making the most of ability, with the goal then becoming something fleeting, such as fame, money, the physical medals, et cetera.
Of course, to reach fruition as an athlete, we must train! It has been said that "the will to win is not as important as the will to prepare to win." To take this further, the will to prepare to win is not as important or as fruitful as the will and knowledge to prepare properly.
I was a witness to extreme cases of poor pace judgment on more than one occasion. In one instance, a runner asked me to act as a rabbit to help him manage his pace during a session of 6 x 600m. He did this specifically because he always ran too fast at the beginning of his workouts and his races and he wanted to try to correct this error. On our very first 600, he sprinted ahead of me and I yelled at him to stay behind me. Despite the fact that he knew of his usual pacing mistakes, and despite the fact that he had enlisted me to serve as his rabbit to prevent those mistakes, he continued to run way too fast on the first 600, finishing over seven seconds ahead of my correct pace. His second and third bouts were slower, and he had difficulty staying with me. His fourth rep was his last. He struggled from the first 100, and by 300, he had fallen off the pace. In spite of his own awareness of his poor pace management, he still could not find the discipline to follow his own rabbit and had to abandon the workout without getting much good out of it!
It is said that Ron Clarke also needed this re-education at one point in his career. Having been introduced to easy running, then progressing to steady running at a faster pace, he was able to become fitter - and ultimately faster - than he had been previously.
Recent race performances or time trials are also good barometers for assigning target paces for workouts. These can be used in conjunction with other data (HR, etc.) and the numbers cross-checked to ensure the pace guidelines are the right ones. For race-pace work, a loud "beeping" device can be set to beep at regular intervals, and cones placed along the track (or other course) every 50m or 100m so the runners reach the cones when the beeper sounds if they are at the proper pace. This device should be placed in the center of the field as opposed to one side of the track, so as to keep the time the sound travels to each cone as consistent as possible.
Yes, use of "feel" pace management is normally done with outings which remain at or below the athlete's threshold. Most of these sessions occur during a period of general conditioning, in which specific speeds can take a back seat to acquisition of fundamental fitness. As you are probably aware, some runners have trouble staying slow enough even when no minimum pace guidelines are imposed! These aspiring athletes certainly need teaching, lest they squander their time spent running! As a period of specialized conditioning approaches (where familiarity with race pace is paramount), many methods and mechanical devises exist which can assist with pace management.
I believe the winning mark was 27:46. Bedford was all over the track that day, visibly overstriding at points, and refusing to relinquish the lead in the early and middle stages of the race. At one point, he even bolted so forcefully around another runner who had briefly taken the lead that he stumbled slightly and veered to the inside of the rail for a couple of steps. Bedford was a tough, brave runner, but his tactics in that race were atrocious.
Yes, I have also recommended that an athlete have a day off - even a scheduled day off every two weeks (or at a different interval) - and count 90 miles in six days as having the same benefit as 100+ miles in a full week. The therapeutic effect of the rest day is sometimes as beneficial for the athlete as running those extra miles.