Thanks to the independence of IP addresses it is possible to change a service provider without interruption as well as to avoid changing public IPv4 and IPv6 addresses (readdressing) in the whole network.
Independent IP addresses also allow implementation of fully redundant connectivity through two or more Internet service providers (multihoming) or optimal distribution (balancing) of the load among multiple lines (load balancing).
Independent IP addresses can be also used to extend the existing IPv4 address space.