Routers don't just need to exchange routes, they also need to actually forward the traffic.
The results of routing decisions are not stored in the packet in any way, so ALL the routers along the path need to know a route that will successfully deliver the packet to it's destination without it getting caught in a routing loop.
iBGP is the normal way to distribute information about external destinations to routers within a AS.
In your diagram R10 and R11 don't really need to know about individual external routes, they only have a single route to the outside world, so they can simply be configured with a default gateway.
R3, R4, R5 and R6 definitely need to know about external routes, so that when they receive a packet destined outside the network, they can send it towards the correct exit.
R7, R8 and R9 could benefit from knowing about external routing information but it's less critical. They could simply be configured with default routes pointing towards R5 and R6 but it may result in less efficient routing and less resiliance against failed links.