Just my two cents as an airline pilot (though not DL):

It's a little more complicated than just having a fully rested crew keep flying as much as possible. Sure, if the crew is on a "reserve block" then they can be flown as much as contractual and FAR limits allow, up until their "off" days. If the crew are considered "line holders" then once they complete their originally scheduled flights and returned to base, or their contractually reassigned flights that fit within the original "footprint" of the original trip, they are off duty. You just can't keep them going forever. And once it gets to a situation where the footprint of the original trip has ended, at least at my airline, the crew is not obligated to work a new flight, and must be deadheaded home. Again I don't know the specifics of DL's contracts, but as you can see it can get very messy very fast.

Thankfully I wasn't caught up in this. But am surprised at the lack of an "Update from Ed" email.

My advice to anyone stranded at an airport: At this point I would book whatever flight you can on another carrier even if it's 2, 3, 4+ days from now and find an acceptable hotel to settle in for the long haul, even if it's a distance from the airport. Standing in line to talk to an agent isn't going to be the most successful. Once the travel has ended submit refund requests to DL for the unflown segments, try to collect on any credit card or 3rd party travel insurance (which in my opinion will be unlikely to be successful and denied or just stuck in an endless loop) and move on. It's going to take DL around a week to reset from this. Hopefully DOT will one day provide more rights for US passengers in situations like these, but sadly we are mostly all on our own.