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?

Totally this. If you’ve got somebody who is critical to the success of the business you do anything you can to keep them

It also buys them time to figure out if you really were critical and see who steps up to replace you. If at the end of the sabbatical you really were irreplaceable, they can fight a lot harder to keep you.

This happened to me. I ended up coming back and deciding I still needed to quit, and the CEO was understanding.

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

Was Andrej in to competitive programming?

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.