When your cluster spans multiple nodes (physical machines, virtual machines, or containers), newly split ranges (or more specifically, replicas of these ranges) are automatically rebalanced to nodes with more capacity. Writes addressed to a range are handled by the Raft leader for that range (which can hop around its various replicas as needed). Writes to different ranges (non-overlapping key spaces by definition) are processed independently, and very well may be processed across multiple machines.
Source: https://www.cockroachlabs.com/docs/stable/frequently-asked-q...
WRT to the writes here, if a majority of the replicas for that range are in the proximate regions, the requests would only travel that far before responding. I believe the argument is that this a more flexible design point than a single point of entry for all incoming writes, regardless of the origin. The cost to write out to the furthest region within any majority of replicas is of course inevitable to have cross-region durability, alternatively you could trade this off to have the majority of your replicas specific to requests from a specific region, be located to that specific region.
