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.
Any kind of "You must find X (x>1) results meeting condition Y" is not progress free. Rather than being like a lottery where you win instantly by chance even if you just make a single lucky roll with probability linearly proportional to how much you play, these patterns accumulate work and as a result faster participants have a much more likely chance to win compared to normal mining.
If you're not seeing that, imagine an extreme case where you must have a billion difficulty-one solutions to form an acceptable block. In that case a miner with 40% hash-power would win virtually every time against a number of other miners with 10 and 20%.Now I understand. It's easier to see in the extreme case. Thank you.
if 10 non p2p type pools control 99% of the hash rate, miners have very few choices in terms of what transaction inclusion policy they want to support with their hash power.