“why can’t we have all the mitzvos and still have separate jobs?”
Kohanim and Leviim (even b’chors and other categories) have different Mitzvos than others. There’s no reason why men and women shouldn’t, also, have different Mitzvos.
Yisroelim shouldn’t be saddened over the fact that they don’t have the same greater responsibilities and Mitzvos as Kohanim, and women shouldn’t be saddened over the fact that they don’t have the same greater responsibilities and Mitzvos as men.
I will add a side point in that I believe the fact that this bothered you, more than a Yisroel is bothered that a Kohain has greater responsibilities, obligations, Mitzvos and receives more Kovod (honors) than himself, is primarily due to the negative influences on the world (over the last 100 or so years) from the terrible feminist/women’s liberation movement. It affects people without realizing it, even those who think they’ve been immune to it.