Although they could be made to run a packet sniffer, which could provide useful information.
But the traffic between nodes is encrypted. All they may get is the previous node's IP address....then they have to start over. Go find that node operator and get them to do the same.
The Tor project does a lot of work to make operating an exit node safer and less likely to prompt the authorities to intervene. This is good, because even if the authorities did want to talk to exit node providers, those people _couldn't_ provide any useful logs.