I'm concerned it could give even more power to those giant miners that already concentrate the hashing power of the world.
That's not really how the system works. There are no "giant miners", at least not from what we can see from our own perspective. You are talking about the major pools that are currently running the network. A pool is made out of a lot of miners. This is the current
distribution of hashrate among the pools right now. I don't see a reason for which there would be any significant changes to the distribution due to the halving. Mining is already somewhat centralized.