Can you explain why cooperation still works when you don't repeat partners? (Assuming I've interpreted you correctly.)
The reason cooperative strategies can work is that actions depend on previous actions. If you are not meeting the same partner, then your partner's actions will not depend on your previous actions, and you will always do better by defecting.
Now that I think about it, you are right that for PD, there has to be some one-on-one iteration too. I think my automatic mental model was that agents came together and played a few rounds with one partner, and then switch to some other partner.
In this case you can afford to be nice in the first round, and then cut your losses. But even that strategy is only optimal if most of the rest of the community is nice in the first round too. If it is full of defectors, then you should defect in the first round too.
The reason cooperative strategies can work is that actions depend on previous actions. If you are not meeting the same partner, then your partner's actions will not depend on your previous actions, and you will always do better by defecting.