Equanimity is just a method like the others, it has an agenda- the removal of stress, and onlooking equanimity is only effective in relatively few circumstances. Most often ‘fabrication of exertion’ has to be applied. These strategies are of both long and short term types. Substitution of opposites such as contemplation of the 32 parts of the body to remove a mind state of desire is applied long-term, whereas blocking an unwanted thought forcibly is a short term tactic. Both methods have the aim of starvation of unwholesome thoughts by preventing them from actualizing. In preventing a thought from actualizing, the mind-state which gave rise to it is progressively starved because it feeds on contact with reality, just as devas cannot access the dhamma except by contact with the human plane.
“He discerns that ‘When I exert a [physical, verbal, or mental] fabrication against this cause of stress, then from the fabrication of exertion there is dispassion. When I look on with equanimity at that cause of stress, then from the development of equanimity there is dispassion.’ So he exerts a fabrication against the cause of stress where there comes dispassion from the fabrication of exertion, and develops equanimity with regard to the cause of stress where there comes dispassion from the development of equanimity. Thus the stress coming from the cause of stress for which there is dispassion through the fabrication of exertion is exhausted & the stress resulting from the cause of stress for which there is dispassion through the development of equanimity is exhausted.”—-MN 101
Inappropriate application of equanimity results in starvation of the investigation factor of awakening;
"And what is lack of food for the arising of unarisen analysis of qualities as a factor for Awakening, or for the growth & increase of analysis of qualities… once it has arisen? There are mental qualities that are skillful & unskillful, blameworthy & blameless, gross & refined, siding with darkness & with light. Not fostering attention to them: This is lack of food for the arising of unarisen analysis of qualities as a factor for Awakening, or for the growth & increase of analysis of qualities… once it has arisen.”—-SN 46.51