Still I can't see why nodes would try to put more PoW into their transactions. Looks like it is enough to submit minimal PoW and have others confirm my transaction with their PoW. It is in the common interest of all users to have more PoW on the legit branch to secure the network against doublespends, but individual interest, it seems, is not aligned with the common one.
Minimal PoW is enough, we assume that there exist a constant flow of new transactions which is a pretty reasonable assumption.
I hope the change is deterministic? Otherwise we'll end up having many conflicting "fixes" of references.
The change is not deterministic. No conflicts are created if there are several fixes, because the transaction data are not changed. It's just copied several times.
This raises another concern. What if a malicious node changes references of a third-party transaction before forwarding it to peers? Different nodes will receive different versions of the same transaction that differ only in references to parents. Also, if references are not secured by signatures, nor by anything else, is it possible to reorder and even censor old transactions, thus changing the graph structure?
Several copies of a transaction increase security of the network, not decrease it. I think there is a confusion caused by different terminology. Let's call data required to be signed (amount, beneficiary, etc.) a
transaction and the part that contains references and the transaction an
envelope. Envelopes reference each other, their sole purpose is to help to achieve consensus, transactions do reference each other indirectly by using outputs of parent transactions as inputs of child transactions. An adversary can't change references inside transactions, anyone can change references inside envelopes but this will only create the 2nd envelope. To be able to censor transactions you need to conduct a successful global eclipse attack, if you only change envelope then you contribute to network security increase. Note, that references inside envelopes are secured by PoW. If you spend electricity on PoW you just make tangle more tangled, which is good.