(Picture from Wikipedia)
While I can see that this makes sense for understanding individuals, the theory is intended to apply to groups and in particular helps us to see how we build stereotypes - for instance we would expect a welfare recipient to be in the lower left quadrant and we expect a less warm, less competent person.
The question occurred to me as to what would happen if we examined the stereotypes pertaining to women and fortunately the study (or studies perhaps) have been done. This is the picture I found
It comes from here and it attributed to T Eckes (2002) Paternalistic and envious gender stereotypes: Testing predictions from the stereotype content model. Sex Roles 47(3-4):99-114.
It is interesting how most stereotypes are found in high warmth OR high competence. I'm not sure what it says that the high warmth- high competence stereotypes are named 'society lady' and 'confident type'!
But this does help us see what stereotypes women are having to overcome in order to be admired! I don't think we can stop stereotypes being formed (because we can't cognitively deal with the number of individuals that would need to be processed) but we can encourage people to be open to the fact that stereotypes do not hold true for all members of a group.