It's already happening at MTV.
The special word for the female actor began disappearing a while back, as if "-ess" is demeaning. We don't say "poetess" anymore.
But does that mean different categories are bad? The roles — other than very minor roles — are almost always written in gendered terms. If a requirement of equal numbers of male and female nominees and an award for both a female and a male were to end, what would happen? Given the kinds of roles that male actors play, I think it's quite likely that they would dominate — not as much as males would dominate in sports if gender separation ended — because they tend to get bigger roles, with a wider range of things they get to show off their powers doing.
Here's the full list of actors who've been nominated for Oscars for leading roles (with the winners identified), and here's the corresponding list for actresses. Try to imagine different years with the categories merged. In 2012, poor Jennifer Lawrence as Tiffany Maxwell in "Silver Linings Playbook," would have had to duke it out with Daniel Day-Lewis as Abraham Lincoln.
And think of the fights we'd have to have. We've seen the #OscarsSoWhite criticisms of the unequal treatment of black performers. Obviously, we don't have separate racial categories for the awards, so the disparities show, though they are complicated by the unequal numbers of people of different races in the United States (and the UK). The merging of the gender categories would put disparities in a stark light, given the equal numbers of males and females in the population. There's an expectation of numerical equality, but I don't think that's what we'd see. It might be good to see that disparity and have more conversation about it.
But I think the separate gender categories for the awards are better for women, mostly because movies tell stories and the stories involve gender roles in endlessly complicated ways. We'd be distracted and confused trying to talk about what kind of equality we want, and I think the stories would suffer. Movies are bad enough already. It might be even worse than merging men and women in sports contests. At least in sports it might be possible to measure the competitors in some scientific way and assign them to different classes — weight, muscle mass, etc. etc. You can never do something like that in art.