The block has to be accepted by all nodes (consensus). Proof-of-work is one such consensus scheme: nodes on the Bitcoin network verify that block hashes are valid and meet the required difficulty. You're suggesting proof-of-bottom-50% for the altcoin reward but there is no viable verification method for it.
E.g. if Antpool mines a block Coinbase has to accept it otherwise you wouldn't be able to transact those mined coins with Coinbase.
block_1 - antpool mines this altcoin block, because they mined bitcoin block_1
block_2 - pool-x mines on top of block_0, because they will check last 144 blocks and see antpool already mined say, 20% blocks. top 50% pools consist of 3 pools; antpool (20%), pool-y (16%), pool-z (15%).
antpool really gains by splitting into 2? I am not arguing. just clueless.
This is an altcoin, with its own consensus and enforcing nodes.