Could the problem of consolidation and concentration in the Bitcoin miner base be solved in the following way?

Design a program that can run in the background on standard desktops, laptops, smartphones, etc., that uses their computing power to turn them into mini mining rigs.

The program automatically connects each device to all other devices running the same program, and the result is the creation of an enormous (in terms of numbers of machines) mining pool. Perhaps millions of devices might run the same program, and the total computing power of all these interconnected devices could be significant from a Bitcoin mining perspective.

The Bitcoins mined by this mining pool are divided among all devices running the program according to a predetermined formula. The Bitcoins awarded to each device are automatically deposited in a wallet that is part of the original program that was downloaded to that device, so the user who downloads the program needs to have no knowledge about receiving or sending Bitcoins. The user receives the Bitcoins directly to his/her device automatically solely as a result of running the program.

Though the amount of Bitcoin received by each device is infinitesimally small, the user receives the Bitcoins for free merely from downloading and running the program. This is one incentive for downloading and running the program.

The other incentive to use the program is to help protect and further the Bitcoin ecosystem by keeping the Bitcoin miner base as broad as possible, and to prevent over-consolidation and over-concentration in the Bitcoin miner base.

Is something like this feasible?