Yeah that's true. You need the data from both the ISP and reddit, and correlate using timestamps from both sides. That's true of VPNs, too. If multiple people with the same external IP were browsing reddit around the same time, the argument in court would likely become about the accuracy of timestamps.
Wouldn't that just consume absurd amounts of storage? Almost every device in my house constantly does update checks and many other connections, keeping track of every connection sounds extreme
3 IP/port combos (internal address, NAT gateway, destination) and a timestamp is ~110 bytes. So for, say, 1 million distinct flows started per customer per day, that's 110Mb.
So no, storage sounds relatively reasonable to me so long as the retention period isn't too long.
If not for law enforcement, at least so they can track you better and sell the data.