The reason why best solutions come when we are solving problems for others is: We can focus more without getting as emotionally involved as we do while solving our own problems (I do understand that some of the problems need ‘emotional involvement’ in order to be solved correctly. Even if we get emotionally involved when solving the problems of others; it does not make us as desperate as when we are doing it for ourselves.
If you have ever paid some attention to the lives of charismatic individuals (I recommend reading ‘The Theory of Prophetic charisma’ if you have not already read it or some other similar profound book!), you might have remarked on the fact that all of them have been extraordinarily detached from others. In spite of that detachment, seemingly very rude and cold, they have come up with some of the best solutions for the problems of mankind.
The Drashta Effect:
Whether you read your own thoughts and feelings or you look back at your thought stream or describe it; it makes you look back at yourself as if you are looking back at someone else; this in turn makes you ‘detached’ from yourself and hence you get best insights and most creative solutions because the ‘emotional patterns’ which pop up as soon as you get attached to yourself, your feelings are not there to hinder your creative thought process.
So: The empirical findings that you work brilliantly when you are solving the problems of others are indeed in alignment with the efficacy of ‘Detached Drashta’ theory. I do not know how long this discovery has been there but I have known it since very long!
The reason why preachers and Gurus (especially here in India) have such a great following is: They are, very often, very brilliant and have solutions to almost all problems of their followers. Without giving much to their being ‘miraculous’; a simple explanation is that they are consistently giving lectures on problems, describing it to others. They listen to the problems with which their followers come to them and then try to give them solutions (this they do with complete detachment). No matter with which level they start: They are bound to become geniuses (or at least experts in certain fields) after a few years of practice of Guruhood! So, in a way, like writing a book or teaching a subject; becoming a Guru is also a simple way to become a genius or at least an expert! Gurus do spend some critical part of their lives in seclusion, which is, quite early in their lives and this in turn makes them use Introversion. Introversion is the meditation on your own thoughts and feelings, which reinforces more and more awareness and hence capability to solve problems.
Gurus often involve in a Socratic dialogue with their followers. This reinforces the true education. The best insights come out of Guru-Shishya pair when some original questions are posed and contemplation is done based on free-association.