I fail to see how that solves anything - it's still not equality, it's just putting the boot on the other foot. A female dominated society like that makes me just as mad as a male dominated one.
In the society I described, a man can leave his property to a woman. She can then dispose of it how SHE pleases. That seems more like equality than the scenario above.
Oh, not saying it solves everything. Not at all. Inequality is inequality. But given that the excesses of patriarchy are often explained, even excused, by the "need" for men to know that the woman/women he supports are bearing his children, it just seems logical that other socioeconomic systems might evolve that bypass this issue in varying ways.
And in fact they have, in other animals, and in some human societies too. Though humans seem to default to patrilineal and patriarchal societies a lot of the time.
My point, though, wasn't to suggest a utopian alternative (I don't think one would exist in any case). Just to point out that the need to control women sexually more than men is no more "logical" than many other alternatives.
Obviously, you have to write things the way they were historically in Egypt, since that's the setting of your story. And yes, it was a better place to be a woman than many other ancient societies (Athens, for instance). But people are often unaware that other systems have existed, and still do in a few places.
And while far from perfect, a matrilineal inheritance system does have the advantage, at least, of allowing both genders equal levels of sexual freedom. There is, in essence, no such thing as a bastard, since a child gets its status through its mother's line, and maternity is far less likely to be uncertain. This doesn't mean there's no sexual jealousy or that couples would never fight over infidelity. Just that a man's sexual jealousy would carry no more weight socially than a woman's.
The thing is, in romance, regardless of the power structure of the relationship, 100% across the board equality in all matters is probably rare. I don't think of my husband as a domineering sort. We have a very equal relationship overall (possibly because neither of us is very good at leading or following). But when I'm watching TV with him and he starts changing the channels around so he's watching two or three shows at once (which drives me nuts), I get up and leave rather than grabbing the remote and telling him to cut it out. I don't do this because he's the man and it's his right to control the remote. I do it because my interest in TV is already so slight that it's just not worth it to me. I get up and go back to the computer, or go back to my book or whatever.
I think a lot of the choices couples make are based on what each person thinks is most important to them. Of course, one's perceived social role may drive these interests too, but that's another story.