Sure it does. How doesn't it?

Egalitarian: relating to or believing in the principle that all people are equal and deserve equal rights and opportunities.
"a fairer, more egalitarian society"

Equal rights and opportunities for sexual pleasure in a romantic relationship.

Equal rights, responsibilities, and opportunities to contribute to a family and household.

Equal rights, responsibilities of parental care for children.

Equal rights, responsibilities, and opportunities for familial assets.

Equal rights and opportunities for decision making.

And so forth and so on.

Interestingly, you'll note that egalitarian principles don't have to be bound to traditional gender roles, but they don't exclude it either for those who want to arrange things that way. It's all in how you value things between each other and then treat each other accordingly.

I disagree with you. It's absolutely necessary for fairness in romantic relationships and it absolutely works.