Routing tables are queried using destination IP of a packet to get the next hop IP and to get the interface to send the packet through.
But since the router will strip the ethernet header first and then process the IP packet and then route. So it will again need to get the mac of the next hop ip for the new ethernet header.
So it will check the arp table and router's arp table also stores the interface along which this mac will be found. So the routing table and arp table both store the interface along which the device will be found.
Is there a purpose other then that which the interface field is needed for? or am I missing a point about it?