The DOT cares little about route overlap for the simple reason you illustrate - network carrier's routes by and large are to and from their hubs and their hubs are not at the same airports, so the routes don't overlap.
However, the DOT is very interested in market overlap. If a combination of two carriers results in a significantly larger share in markets (regardless of the routes used to serve that market), the DOT considers that anti-competitive. They frown at anything anti-competitive.
Jim
While you're completely correct about the distinction between route and market overlap, I'm not as pessimistic about antitrust approval of a proposed UA/DL (or any other combination of two of the big six). Since 2000, B6, WN and others have shown a remarkable ability to enter markets and drive down fares, especially where those true LCCs see the legacies earning high yields.
Granted, this won't help the Podunk-Backwater markets, but many of those are already one-horse (or single engine) towns. A lot has changed since 2000 when rumours of antitrust denial swirled about the UA-US merger, and I suspect similar mergers now would be approved. Perhaps approved with some market/asset divestitures, but approved nonetheless.
Of course, you're probably right (as usual). Cheers.