It depends on the amount of severance and the person. Not sure if everybody would prefer to get a couple months worth of severance but have to go through the stress of quickly finding a new job.

I find that stressful even if I live in a country where I have the same level of healthcare no matter whether I'm employed or not. How do you guys in the US cope with that? Is it as bad as it looks from outside or you have mechanisms to not lose all your healthcare if laid off?

You get severance and can claim unemployment for a while too if you're laid off. Getting people to jump ship themselves avoids severance payouts and UI claims.

If you plan to jump ship, negotiate with HR to get the severance package and voluntary leave, especially if you're hot shit and can get another job quickly, otherwise you're leaving money on the table. The only thing you lose here is eligibility for unemployment, which you won't need anyway.

Healthcare is a shitshow. You can do COBRA, which lets you maintain your health plan by picking up the tab the employer previously paid. I've never done it myself but heard premiums were like $800 per person per month, years ago.