A story is told of a religious leader known to have had a fiery nature during his younger days. Another religious scholar, disguised as a hunter, came upon the man stroking a tame partridge while seated underneath a tree. The scholar marveled over the fact the religious man would 'waste his time' in such trivial activity.
The religious man asked in return, "do you always carry your bow unstrung?" The scholar responded, "no, for if I were to keep it strung continually, the bow would weaken. If I then needed to shoot at a boar or large animal it would no work correctly." The religious man replied, "if the bow that is continually bent will eventually cease to shoot straight, then do not worry about my brief period of relaxation."
It's important for the individual/self-coached runner to know certain things before they begin to develop their training plan. The most important factor is to know how much time they have available to train. The second-most important factor is the event or events which they are targeting with their training. Almost as important as the first two factors is to determine the day (or days) in the week to rest from training.
Professional athletes and younger adults might be able to get away with a seven-day-a-week schedule - but the runner who works a "real job" usually does not have the option of resting when not training. The choice is simple; take time off or risk progressive weakening.
Some running coaches have espoused the idea of taking a day off each week for every decade over thirty. So a 40-year-old would take one day, a 50-year-old two days, and so on. Other coaches "cut-back" training intensities/distances every third or fourth week of training, depending on the athlete. Others have recommended a day off each week, a week off (or easy!) each month and a month off each year. And yes, there are coaches who believe the need for a rest day is proof the runner has trained too hard or running too fast in their training.
The day of rest provides physical and mental recovery from the stress of running. It lets the person have something which vaguely resembles a life, rather than be "just a runner." While the amount of rest needed varies by person it cannot be overlooked completely. The body needs rest and recovery and it will get what it wants, either by choice or by circumstance.