I think that the basic idea of Saitama's power is that it is completely incomprehensible. In other words, it is apophatic - beyond any possible interpretation.
Remember dr. Genus, who conceptualized Saitama's powers in terms of breaking the limiter. What happened next? Garou broke his limiter, but he didn't get Saitama's power.
The other thing is that Saitama is a very absurd character because he is always balancing on being very obsessed with his everyday life worries, but we know that he is a real hero and that he is very serious about his hobby, and we know that he is a virtuous person in reality. Moreover, he is totally not included in the social environment in which everybody leaves, he doesn't even understand it, that is a consequence of his true internal asceticism.
What is interesting is that Genos, his student, is doing pretty well in imitating Saitama in this respect, so Saitama is also a good teacher, even though he doesn't understand it either, because he doesn't really care.
So, I think that Saitama is actually an enlightened prophet, whose powers and their source are beyond any possible conceptualization (which is a very Buddhistic idea). He is free from desires, he is virtuous and he is not integrated into social network properly. But the difference between Buddhistic philosophy and Saitama is that he actually is still suffering, even though he has no true desires. So maybe there is a deeper idea here, that Saitama is even more ambivalent than Buddha.