1. It is primarily about the Bitcoin core, and not about mining
^ here is your issue
meaning the rest of your topic post is about DISTRIBUTION not decentralisation.
imagine a bug needing a recall of devices. or a firmware update. if everything is core then the recall/update ends up coming from a single central point
its the same as demanding all computers only run microsoft
As far as I know, the Bitcoin core is reliably verified and no errors are detected there and will not be detected with high confidence.
As for mining, you can make a separate game with a mining unit for those who want it, but it is better to do mining on the game server. Hardware requirements for mining and game server are similar, and it is quite possible to combine it.
Although there is another option (I wrote about this earlier), you can make mining distributed over a large number of gamers (pool of gamers-miners)
In order to stimulate gamers to give the mining unit in the game to work, while the gamer does not play, you can make a special bonus that is spent while the player is playing and recovering, while the player is not playing, but the game is not closed.