Was it by design or accident?
Arbitrary choice, it's unlikely satoshi performed research about effect block propagation on different block time.
Can't we just make it quicker and reduce the rewards appropriately?
You can, P2Pool did just that, they reduced it 20 times, reaching 30 seconds per block.
Do you mean P2Pool the decentralized mininig pool? If so, i'm sure it refer to how often the "share" is updated.