Amida Buddha is a product of the quest because Amida Buddha is the culmination of perfection of wisdom and compassion. When we enter Nirvana we enter enlightenment. The Pure Land practice is a chosen practice because those with even a inferior capacity can become Buddhas. People in their day to day follow a non-monastic life. Nor is it possible to practice religion on the path of sages since we are committed to our lives as we are on a day to day basis.
Many people have inferior capcities.
Therefore they must rely on faith alone. Everyone has a inferior capacity for enlightenment, because no one is any better than anyone else. In which case, people must attempt to find enlightenment on faith alone. This is called Jodomon. That is opposite of Shodomon, the path of sages.