While it may seem logical to give away empty first-class seats to passengers in lower classes to increase customer satisfaction, there are several factors that contribute to why airlines typically don’t do this:

1. Revenue Management: Airlines carefully manage their inventory and pricing to maximize revenue. First-class seats are typically sold at higher prices compared to business or economy class. By giving away those seats for free, the airline would be forgoing potential revenue.
2. Premium Service Differentiation: First-class cabins offer premium services, amenities, and extra space to passengers who have paid a premium price for those benefits. Giving away those seats would diminish the exclusivity and differentiation that first-class passengers expect and value.
3. Loyalty Programs: Airlines have loyalty programs and elite status tiers that reward frequent flyers with upgrades. Giving away first-class seats for free could devalue these loyalty programs and diminish the incentive for customers to reach higher status levels.
4. Operational Considerations: There may be operational reasons why an empty first-class seat cannot be given away. For example, weight and balance considerations are important for aircraft performance, and moving passengers to different cabins can impact these calculations. Additionally, there may be security and regulatory requirements related to cabin assignments.

That being said, some airlines do occasionally offer paid upgrades to passengers in lower classes, especially if there are unsold first-class seats close to the departure time. This allows the airline to generate additional revenue while still providing an opportunity for passengers to experience an upgraded cabin.

Ultimately, airlines must strike a balance between revenue generation, customer satisfaction, and operational considerations. While giving away empty first-class seats may seem like a straightforward solution, there are various factors that airlines take into account when making such decisions.