Your suggestions are unfortunately infeasible, and pooled mining exists.

Why should the reward be split among the miners when the ones with more hash-rate will generally have a higher chance of acquiring the block(s), and thus it balances out?

Also, pools split rewards within the pool depending on individual hash-rate contribution, that's the closest you'll get to a split in the mining world, and its only within the pool, there are multiple pools.

The system is fair, and regardless of it being chance based to an extent, the higher hash-rate miners will still in the long-term acquire more blocks (well to be fair most of them are pooled, so lets say Bitcoins rather than blocks).

Currently, the majority of blocks are discovered by pools, and then split among the miners depending on contribution.

What you are suggesting is some sort of pooled-mining system where only the top 100 highest hash-rate miners get any kind of reward, why should they share their block if your system would be implemented?