A couple of theories:

1) It sometimes can be hard to leave a company when you are "in the thick of it." A sabbatical can give you personal time to reflect on whether you want to stay or not.

2) Sometimes people use sabbaticals to prep/perform job interviews or plan career transitions.

3) Sabbaticals can allow you to quit early while waiting for vesting restricted stock units, employee stock plan sales, retirement contributions (matches), etc. There are certainly many more timed bonuses available for senior leaders.

Employee: I quit.

Employer: Are you sure? Why don’t you take some time off and think about it?

He needed some time to get up to speed with leetcode ;-)

At some companies sabbaticals are an explicit part of the benefits package. Every X years, you'll get a paid sabbatical of Y months. If you're close to X, why not wait and get the Y before you leave?

When a key person leaves, a lot of things can go haywire. If they take a break first, they can be semi-available to help resolve the most urgent issues. Kind of like turning off the circuit at the breaker to find out what is plugged into it.