Isn't that what mining pools are doing? Collecting the all the possible hashing power and rewarding the community for their contribution? Anyhow, this can't be done with a just mobile phone or any low specs computer because the difficulty rate is very high.
it seems you yourself in the third sentence contradicted your first and second sentences.
I think the OP may be onto something, and I encourage him to follow his idea. If he reads the comments of the critics carefully, they are all very good and valid points, and I encourage the OP to read them not as points that must be downplayed in order to prove his idea is right, but rather as indications of weak spots of the idea that may need some more thought and enforcement before the idea can be accepted by the community.
No, I am not contradicting anything. I am just indicating the problems it will encounter with this kind of Idea. Idea is good but the implementation might need some considering.