> Thus, as a miner, I have an incentive to spam the block with transactions in order to increase my chances to winning the satoshi.
Spamming the block with transactions does not increase your chances of winning a satoshi, because all satoshis have equal probability of winning, regardless of which utxo they are in, or how many utxos they are spread across.
It sounds like you are thinking that every *utxo* has equal probability of winning. This is not the design I am describing. In this design, a utxo containing 2000 satoshis has twice the probability of being picked than a utxo containing 1000 satoshis.