Technical question about block reward

I have a simple question about the block reward and the halving event. Is there a reason that the halving happening every 4 years is setup in a singular event. Why the halving phenomena is not distributed within a 4 years span, each block reward is just a little bit less then the previous. The result would be the same, after each 4 years the block reward would cut in half. it would be a progressious halving phenomena instead of a discrete one.

I didnt do the exact math but it would look like that.

Nov28, 2012. Block reward 25bitcoin.... the next block reward: 24.999 bitcoin.... the next block 24.998 etc....

thank you community!