Without a block reward, you are correct that the only incentive to be on a longest chain is so your transaction is confirmed unambiguously.
There are still transaction fees to consider (although obviously not in Iota), otherwise you might argue that bitcoin itself would suffer the same fate of diverging consensus, when the block reward expires.
And note that if we use Satoshi's design or Bitcoin-NG's design, then transaction fees are problematic because in Satoshi's design we don't know when our transaction will be included in a block because we can't know apriori the minimum transaction fee of the node which wins the next block solution and for Bitcoin-NG that node (which is already known when we send our transaction due to NG's instant confirmations) can extort high transaction fees if we are in a rush because that node has a monopoly until the next block is found. Thus essentially these designs make mining profitable again and eliminate the advantages of including a PoW share with each transaction.
Mining has to be unprofitable for my idea to enable decentralization and fix the "
unbounded transactions spam versus centralized oligarchy mining control tradeoff" dilemma.
Thus I believe my idea can only work in my design which has a difference from those two above. I am trying to find the flaw in my design that renders mining profitable through some game theory. That is why I say I am not yet sure if my idea is sound. In my design there are multiple nodes to submit transactions to, i.e. the intrablock partitions, so they can't monopolize and thus transactions fees should fall to the level of costs. And thus mining should remain unprofitable. There can be complex elusive flaws though, so I need to study my design more.