To me multi-node isn’t about bottlenecks, it’s about reliability and durability. Nodes go down, whether from issues with the underlying server or from an OOM bug or any number of reasons, and if you have multiple nodes up then your load balancer health checks can react and keep routing traffic to good nodes while your bad ones come back online or are replaced. If you only have one live node then when it goes down your system is simply down until you get it fixed.
This is why I think for this particular problem at least, the client side is the right place to store this info.
