I don't have experience with airline scheduling but I have experience with software in large financial corporations like banks. The situation with banks (at least the ones I worked with) is that there is a huge amount of software maintained mostly by mediocre to bad teams. These teams fail a lot, the software fails a lot, and yet everything seems to keep going.

It is not about code or algorithm quality, it is about procedural side of things -- how the organisation is "programmed" to respond to failures. I use the word "programmed" in a very broad sense -- for me setting up a paper checklist and being able to rely on people to follow it is the same as programming.

I suspect the main difference between airlines and banks is that banks can afford to throw money on the problem and just get things done regardless of how inefficiently.

Airlines are in the much worse position -- they were able to afford being inefficient and throwing money at the problem in the past but can't do it anymore. They work with old, outdated software that wasn't built with efficiency in mind but now don't have funds to change it and are forced to maintain what they have. This may also be the answer to why sometimes they just don't have capacity to react to problem and let it cascade to bring everything to a halt.