This is the first explanation I've seen that fits the odd facts perfectly. This is the kind of thing that happens when two regional bureaucracies collide. The FAA has long-standing mechanisms for coordinating military use of airspace with commercial and civilian flight operations.

But instead of the usual DEA border interdiction, the administration is now tasking the military to drive this. Military commanders on a new high-priority mission to intercept drones which can attempt to cross the border anytime and anywhere realized coordinating with the FAA would require committing to active corridors and time windows in advance, limiting their mission success and resisted. The FAA realized that could lead to lots of last minute airspace restrictions, flight cancellations and increased risk of a mistake resulting in downing a civilian flight.

The regional FAA administrators responsible for flight safety around El Paso decided to escalate the dispute by simply shutting down all civilian flights, knowing that would get immediate national attention. It was an extreme action but one that's within their purview if they can't guarantee the safety of the airspace. I'm sure they expected it would put political pressure on the military to limit operations and it worked. In a sense, it also helps the military commanders because being ordered to accept FAA operational limitations gives them cover if it reduces their mission effectiveness below what they'd promised. That's probably why the military wouldn't agree on their own without it being ordered from above. They're the ones responsible for deploying expensive new anti-drone tech in field ops for the first time. Future budgets and careers are on the line.

It sounds like the DOD was being unusually indifferent to the concerns, and after deadly prior mishaps, the FAA has to be particularly careful here.

Indeterminate end dates are not a new problem.