I almost got rebooked on another airline this spring, but it involved a ground stop in Atlanta in addition to our MX delay and the first level customer service having to punt us a few levels higher when her screen said they couldn't get us to Scotland for another three days. It would have involved going from Florida to the UK by way of San Francisco, and after we kind of balked at that one, a nice and competent person named Robin let our deep discount coach fare change to a Y fare, and we ended up on DL metal going through Boston instead and only losing a day of vacation.

So my guess is that it's possible but it takes a hellava unrelated mess for it to even be on the table these days.

Back in pre-merger ancient history, I got DL to rebook me on Northwest when a baggage train thingie (what's the proper term for those guys?) clipped the wing of our RJ hard enough to dent it, and it took an more than an hour for the 'on call' mechanic to make it to the airport, resulting in me missing my connecting flight. Twas a different era back then.