Traceroute doesn't use ping requests except with the old Windows binary. Usually it uses "Time-to-live (TTL) exceeded in transit" messages.
Beyond that technicality, your guess is often right... Routers will frequently prioritize forwarding packets over sending the TTL exceeded packets tools like MTR use to measure response times.
Also you can easily have the TTL expired message going via a different route on the return path (and indeed the same applies with your normal connections, asymetric routing can be a pain - especially in networks with rpf issues (multicast ones are a particular pain point), and with stateful firewalls, but most of the time it's fine. You just need to be aware.
Obviously you know, but for anyone else reading, a modern traceroute tool (like mtr) can send icmp, udp or tcp, on generic or specific ports. Indeed the default for mtr on my laptop is to use icmp.
Beyond that technicality, your guess is often right... Routers will frequently prioritize forwarding packets over sending the TTL exceeded packets tools like MTR use to measure response times.