I know it's not really a completely random selection because some miners have more hashing power so their odds are increased.
But let's assume for a moment that all miners are about equal in hashing power.
The way I see it, whoever solves the current block is (almost) completely unpredictable and thus mining is just a way to randomly select a winning miner.
I understand about decentralizing and the need for a decentralized way of selecting this winner without trusting a higher authority for this random selection.
Let's imagine for a moment that there was this "god-like" machine somewhere, completely trustworthy and incorruptible, impossible to bring down or shutdown and completely fair. Let's say this machine would select the winning miner that would create and sign the next block and get the reward and fees.
Would there still be a need for mining in that case?