It depends how supply and demand curves are moving. What might be true today may not have been true 10 years or 20 or 30 years ago. Labor costs have a big impact on profit, a measurement that all company owners and executives care very much about.
For the past few decades, it may have been true that the cost of attrition was less than the benefits of holding down pay for most others.
I am sure some businesses got it wrong, and some businesses got it right. And it probably even varies within businesses based on specific roles.
For example, it very well may be rational for a grocery store to let cashiers go if the cost of acquiring and training a new one is low enough that it lets the store compete with other grocery stores since they are operating on razor thin margins. On the other hand, people with specialized tasks in the store such as a butcher or baker or manager might have a better case for keeping them from leaving.
People aren't rational actors in the sense of "they aim for the objectively best action given a goal" - we generally aim to minimise risk, prefer things that are simple, and prefer doing what everybody else is doing. Homo economicus isn't even used in modern economics let alone being anywhere near to reality.