This isn't a need: miners will contribute to the highest work braid/chain simply because that is the one most likely to have other people contribute to it. No extra incentive is needed. If there exist two childless beads (blocks), it's in my best interest to name them both as parents. That generates a higher work braid. Naming only one of them creates a lower work braid.
This is not that simple, as Selfish Mining paper showed, a more sophisticated strategy may be more profitable.
Selfish mining works because of the asymmetry between profit of a block that gets orphaned and one that ends up in the main chain. There's no reason to have orphans at all with a braid. Withholding a block doesn't buy you anything.
This is a concept I put forth in my most recent talk about braids: "equal pay for equal proof-of-work". Selfish mining is killed by a combination of braiding (no more orphans), and removing the asymmetry by ensuring all valid PoW hashes earn a block reward.
that rewarding all branches makes a 51% attack free.
Even with or without direct monetary rewards (e.g. minted coins or non-burned txn fees), selfish mining can be conceptualized more generally as the asymmetry (for different proof-of-work participants, aka miners in Bitcoin) of the cost of effective PoW (or burned txn fees), for whatever PoW (or burned txn fees) accomplishes in the consensus system. So even for Iota or DagCoin which afair don't monetarily reward the PoW (i.e. afaik the PoW is simply burned), the asymmetry still exists in terms of the value of what PoW can effect in the system. Thus as CfB wrote, "
a more sophisticated strategy may be more profitable" given some externalities such as achieving a double-spend and shorting the token's exchange value.