While the host has some information about reachability of src/dst locator pairs, it does not have information on how this maps to the exit paths from the site. For instance, if the host could choose between 3 destination locators it wouldn't know that for instance the first two result in the same exit path being used. That level of information is known in the routing system.
Why do you think host can not get infromation from the routing system?
In good old days when IPv4 routing table was not bloated, it was usual for UNIX box to run routed (in quite mode) even if a host is singly homed.