Other airlines aren't why Spirit failed. And Southwest would argue as to who invented the LCC model that Spirit copied.

Spirit has a singular market niche (low budget travelers) and is too slow in pivoting to capture other sources of revenue. Its business model is not flexible enough to pivot back and forth from leisure to business to premium to frequent flyers. Spirit went after one demographic, leisure travelers, and did a great job for a while. But more and more passengers are seeking value when they fly. Not just a cheap ticket. Add in the other things like bad reputation, competition, poor management, bad financial decisions (not paying for Pratt engine warranties, etc) have gotten Spirit in the mess that its in.

If Spirit's business model is so fragile that just offering the same fare can put it out of business, it never really had a defensible market strategy. Just an income opportunity that was over-scaled and has run its course. Fortunately the pilots are are skilled and valuable and will end up at other carriers eventually.