Banks for a long time thought the same. Then banking startups with code written on a clean slate in modern architectures emerged and are eating the bank's lunches as their infrastructure (more often than not a mix of mainframe, weird custom middleware and half-modern webstacks) cannot keep up in development pace. For example, in Germany Commerzbank (once a powerhouse) got kicked out of the DAX with former fintech startup now giant Wirecard replacing them.
Airlines are only "kept safe" from modernization because the cost of entry is so unbelievably huge - to start a bank one needs only a couple of employees plus a couple million euros founding money, but to start an airline one needs vastly bigger sums.