To lean into your example: if you want to design travel search, you might envision a system that goes from a user's typed query -> a structured query -> executed against a database of real-time flights -> judging the result for feasibility of the resulting proposals created by those queries.
What you can do with LLMs is reverse this: from any numbers of snapshots of flight data, you can create large numbers of plausible user queries, based on your data, that are known to be feasible or infeasible. And now you have a labeled data set to train a model that focuses solely on the query-creation and judgment systems. And you can experiment with whether having a more flexible query protocol leads to higher success rates without sacrificing accuracy, or whether you can generate that last-mile feasibility check as a combination of auditable code checks alongside AI-based judgment.
LLMs don't absolve you of having to break down your system architectures into components that have well-defined boundaries (though certainly they can help with that design). They do make those components feasible to solve at scale.