Well, they do it most directly because it is a “pen register” as defined in law: …the term “pen register” means a device or process which records or decodes dialing, routing, addressing, or signaling information transmitted by an instrument or facility from which a wire or electronic communication is transmitted, provided, however, that such information shall not include the contents of any communication, but such term does not include any device or process used by a provider or customer of a wire or electronic communication service for billing, or recording as an incident to billing, for communications services provided by such provider or any device or process used by a provider or customer of a wire communication service for cost accounting or other like purposes in the ordinary course of its business;… 18 U.S.C 3127.
You are correct that this statute was created to manage the process related to the exception identified in Smith v. Maryland, but I don’t think that there is a good-faith argument that it is either inconsistent with the scope of the exception or anything except a limitation on law enforcement compared to not having the statute.
I might should make a video and upload it to the Internet Archive, for historical reference. These seem to be rare devices.
[1] https://www.shoghicom.com/fixed-line-lawful-interception.php
The pen register shown in that Wikipedia article is mine. To use it, you need physical access to a phone line, probably at the central office. You put in a blank spool of paper tape, add stamp pad ink to the ink roller, and wind it up with a big brass key. When it detects a dial pulse, the clockwork mechanism starts the tape moving, and each dial pulse produces a dash on the tape. There's a mechanical idle timer which stops tape movement after a few seconds of idle time. I built a box with a phone dial to run that brass device as a demo.
That's what law enforcement had to use in the days of electromagnetic central offices. Only long distance calls were logged. Local calls were, at most, counted. That's why the Supreme Court decision refers to a pen register as an "extremely limited" device.