It's actually a legitimate concern, and it goes far beyond coworkers embarrassing you in slack.
For example, posted yesterday: https://tailscale.com/blog/rotate-ssh-keys/ (https://news.ycombinator.com/item?id=26249380)
> One company had an employee they fired for bad behaviour. A few months later all their production servers got wiped out. ... A month later, it happened again! Everything gone.
> What happened was that the rogue employee, months before they were fired, had waited until everyone went to lunch, walked around from one PC to the next, and collected the ssh private keys from any of them that weren’t locked. ... Then, a while after getting fired, he used a co-worker’s ssh key to login and destroy everything.
Of course, screen locking would not prevent a determined, disgruntled (or desperate) employee from pulling off something like this, but it would stop the casual collection of secrets while everyone is at lunch. Add full disk encryption to PCs and you have a reasonable chance at defending.
Oh, and if you're doing anything with credit cards, PCI DSS requires you to enforce a workstation locking policy. Failing to do so opens you up to massive liability in the event of a breach.