That's a naive solution that has dramatic centralizing effects. By owning more coins, you are stronger than the competition. The miner with the most coins will

That's a naive solution that has dramatic centralizing effects. By owning more coins, you are stronger than the competition. The miner with the most coins will out compete the rest, and you will be left with one miner. This problem has been very well studied and there are not any simple solutions available. Many academics believe that it's fundamentally impossible.