I think your comparison is anecdotal and oversimplified. The two airlines operate at similar net profit margins in a booming economy, so it's all relative I guess. Spirit also has $1B cash on hand, half of what Delta does at a fraction of the size.
The ULCC model in the U.S. hasn't been around long enough to be tested by a true economic downturn, it was in its infancy during the last recession. If consumers are more sensitive to fare pricing than ancillary costs, Delta's margins are more negatively impacted than Spirit's in another recession. The legacies will have to compete with ULCCs on price, but can't compete on cost. The ULCC model is here to stay...until their costs begin to rise and their comparative advantage evaporates. Aircraft age, labor contracts improve, infrastructure is added, etc. Then what, rinse and repeat? A new ULCC startup every few years? Do the legacies just continue to absorb ULCCs after they inevitably bloat into LCCs?