well, none. a route loop mistake involving that router and you’ll have a packet storm that wont subside until the router reboots from the stress.
i’m not as worried about the detrimental effects of traceroute as much as i’m worried about what would happen if the wrong interface (local interface) no longer was in running state. what would happen then is packets from the internet, destined to your network, would bounce between your router and the upstream router (following default gateway) until something broke down.
but you know your network best, of course.