“Hatzur tamim po’alo” Hashem has cheshbonos for everything, & they are good for each person in totality. We may be at a loss to fathom why it is good at our current standpoints, however the ultimate goodness is assured. Consequently, we can daven, and others can daven on our behalf however if this wouldn’t be good for the person (or others and thereby not totally good) Hashem wont let it happen until the time that it is totally good for all parties. Now, part of making it good may be allowing a person to utilize their predicament to grow and thereby thrive form their challenge. Despite this, we the living are unable to know those cheshbonos & therefore need to act accordingly, by strengthening our emuna & bitachon in Hashem, for this may be the road block preventing the desired yeshua. A means to this end is tefila, where we directly beseech our father to aid us. Not that Hashem needs our tefilas, rather by going through the motions, we reinforce these feelings in ourselves thereby bringing us closer quantitatively to our father in heaven.
This brings me to interpret this seminary teachers comments of Hashem wanting a certain amount of tefilas- as Hashem wanting us to utilize this predicament to grow to a new level of ruchnius as an act of chesed to the person.
Thereby its also conceivable that this “greater good” may encompass that Hashem wants one to be the catalyst for another to also grow in ruchnius, and this would need to ultimately be good for both parties.