It took so long to invent Bitcoin because no one before Satoshi managed to make a truly decentralized system without any single trusted entities. Your system seems to introduce them again, because someone will have to organize this whole process.
Only a tiny fraction of the total hash power of the network is saved in the block that gets accepted. Maybe there's a more fair and efficient way to mine.
You're misunderstanding mining. The point of mining is to generate blocks every 10 minutes without any third parties. It's not about "protecting the network" or "backing bitcoins with energy".