I don't understand that if you want to stop or rather feel like you want to stop after 20 minutes then surely you're going faster than your 1 hour pace, ergo too fast...?
My thought is that if a person is going to race for an hour, they spend time physically resting and mentally preparing for that race. At the end of the race, they will be exhausted and need to recover for several days perhaps weeks. An hour race is no joke.
However, for a weekly workout, the preparation (both physical and mental) isn't as focused and targeted as for a race. And the goal is not to run the person to exhaustion, but to stimulate the body to clear lactate, which is why you limit the run to 20ish minutes. The pace, however, is the same as the 1 hour race. That still feels tough after 15 minutes. The difference is that the athlete stops after 20 min rather than completing the hour race. In a race, the athlete would probably not feel that way until halfway due to the added rest, mental preparation, and race day adrenaline. In a weekly workout, you feel it sooner.
Not sure if that makes sense or properly answers the question.