The problem is the proof of work is tied to the transaction that sends the block reward. So, there isn't an obvious way to generate a coherent block using multiple proof of work solutions. So, the ways to make the block reward more granular means more blocks more often. However, there is a tradeoff as each block has additional overhead. So if you change from 10minutes to every 1 second the amount of additional network / computation / storage would make running the protocol much more challenging. So, there is the trade off.
Why not enforce each block to have 25 coinbase tx's to different payout addresses and force the hash of each of those addresses combined with a subset of tx's in the block to be less than a specified difficulty value. Nobody gets a payout until 25 such hashes meets a difficulty threshold.