Interesting take on the strength-warmth framework in a hire/fire/promote context. A challenge comes when you slice a layer deeper along either axis, e.g., with people who are technically competent but not assertive, or who have mission-driven intentions but are not emotionally intelligent in dealing with teammates.
The 2x2 below describes the emotional responses elicited by demonstrations of strength (competence + assertiveness) and/or warmth (shared interests, concerns, and emotions).
It can be useful for reflecting on your own performance as well as for assessing others in a professional context.