From my Cisco CCNA documentation:
Routed ports are used for point-to-point links. Connecting WAN routers and security devices are examples of the use of routed ports. In a switched network, routed ports are mostly configured between switches in the core and distribution layer. The figure illustrates an example of routed ports in a campus switched network.
I don't understand what are the benefit of having a routed port between the distribution and access, and more generally, the purpose of routed ports except for inter-VLAN routing like with the router-on-a-stick method (and even there, it seems that SVI are a better approach).