If the the IP is "the White House" there may be dozens of clients running out that single NAT IP. So you'd need a bit more correlation before you hit all of them with a warrant, I'd think. Some tracking cookie or some ID to show it's the same person behind the keyboard. As the transcript shows, the judge asked about payment (like a credit card # for correlation) but Twitter is free.
Not saying it's a viable technique but I get the idea that judges hate warrants that vague.
Sure, but as others have said, you have device IDs, you have when Trump was traveling and using cellular data, etc. So there is a huge amount of info that can be used to relate accounts.
Legally, it seems asking for a company to run essentially joins across their DB tables is accepted practice. Otherwise, how could warrant be obtained from google for all devices within a specific geolocation? Requires at least a few DB queries I'd imagine.
Not saying it's a viable technique but I get the idea that judges hate warrants that vague.