I think a large part of the reason that men are more likely to end up "on the bottom" of society is that men have smaller support systems/friend networks than women. Some of the reasons for this are stigma against men expressing vulnerability, stigma against men seeking help, homophobia around close male friendships, gender expectations that women should do more "emotional work" than men, and stereotypes that women are social and men are not. Feminism seeks to dismantle all of the above, so in that sense, it would make it possible for men to have much stronger support networks.

Additionally, many (most?) feminists believe in "intersectionality", the belief that sexism, racism, classism, ableism, and heterosexism act in intersecting ways, and that all need to be dismantled together (for instance, this is why most feminists support reform of the US prison system, even though this is something that primarily effects men). Dismantling these oppressive systems would very much help those on the bottom.

The exclusive-focus-on-more-white-woman-as-CEOs brand of feminism is actually a minority of feminists (although they seem to get the most coverage in the popular press) and is widely critiqued within feminism.