This problem exists regardless of PGP. If someone's Slack is compromised:
With PGP: attacker gets credentials encrypted to their key
Without PGP: attacker gets plaintext credentials
But both fail at the same point: verifying who you're talking to. That's not a PGP problem, it's a "doing password resets over unauthenticated Slack" problem.
PGP does provide multiple identity verification mechanisms, e.g. web of trust, key signing, fingerprint verification, in-person key exchange, and Keybase-style social proofs linking keys to verified accounts.
The workflow described just doesn't use them. Identity verification is required for ANY secure credential exchange system; you either verify keys properly (signed by trusted parties, verified fingerprints, pre-enrolled, social proofs) or you have the same problem with passwords, TOFU SSH keys, or anything else.
Are you criticizing PGP for not solving a problem that the workflow simply didn't implement a solution for?