The patriarchy is bad for men too. That doesn't mean it isn't still the patriarchy.
As far as I see, based on my experience, the social drive of 'protect the woman, let the guy rot' is tied up in a lot of things. But critically, I think at least one of these is racism. At least in the West, the default 'innocent woman who needs saving' is a pretty, white, healthy and able-bodied cis woman. And if she isn't one of those things, well, society doesn't spend nearly as much time worrying about it, let alone when she isn't more of those things. And conversely, the social treatment of men that you talk about reflecting "disposability" I think has a lot to do with racism and xenophobia. The default picture that much of the west has developed for the 'scourge of society' is a young non-white guy. In many countries these are also immigrants. When there's a young white guy accused of sexual assault, all anyone wants to talk about is how the allegation will ruin his life; when it's a black guy, he's a "superpredator". And the worst part is that psychological experiments reveal that this bias is even deeper than we might think, and certainly deeper than we want. It's ingrained into society (I don't think there's really a need to posit a biological basis for this), just like we could say the same of its treatment of women.
One thing I think you're right about, women and children are perceived (unconsciously or subconsciously) to be the core of society. But I think one powerful side effect of that is that, rather than 'women serving the male centre', it's actually 'men wanting to control the female centre'. And doing so, quite effectively. As long as there is this continuing pattern of domestic violence and sexual violence that disproportionately affect women, I find it hard to take seriously the argument that society places women (as a whole) on a pedestal when I see so painfully the way in which so many are ignored, or worse, subject to the full, undiluted brutality of society; rather it seems to me that certain women—certainly those with the social capital earned from other positions of power (whether race, social class/wealth, etc.)—are 'protected' from the 'threat' of everything that lies below.
The thing about social contructs is that I think when people say 'gender is (just) a social construct', it's commonly misunderstood to mean 'gender isn't real'. But it is real. Gender is real and race is real and sex is real and social class is real and money is real. But they're all social constructs too: the meaning of all of these things is determined and maintained by society. What qualifies someone as 'white' today in the United States is different from what it was one hundred years ago. Who knows, maybe trans people will eventually have some impact on society's understanding of gender, too—and if so, we might say that the social construct has shifted to include some impact of individual expression.
I don't think it's idealism to speculate on what the world could be like if the rigid division of society on the basis of arbitrary social categories assigned messily to people who have themselves been given bodies that rather messily fit (hence all the exceptions falling out the edges, i.e. us; it's all somewhat random in the end). I'm not sure such things are possible either, in practical terms at least if not in theoretical terms, but that more reflects my pessimism on the world as a whole. I also think misogyny and racism are here for the long haul and will ruin the lives of millions and millions more—hell, probably billions more. And a lot of those people will be men. But in the end, I fight because I think the way things are right now is wrong, profoundly so. So what if some of that reason is bound up in 'human nature'/genetics? I think that's all the more reason to work against it vociferously, because it means that more people will suffer if people don't learn to fight that unconscious bias.
One thing I will say, it's easy to talk about the fact that in much of the Western world, women (or non-straight people, for a similar example) are afforded equal or nearly-equal rights under the law. But what is the case under the law does not match fully with what is the case in fact. If a company can get away with paying you less as a woman (and you don't have the money to sue), then all the laws in the world won't change it. What is a full slate of reproductive rights if it's only afforded to the people that can afford it? If you can't report a case of sexual assault or domestic violence because the police won't believe you, what does it even mean that rape is illegal?
These are heavy topics, but I don't bring them up lightly either. For me, for my personal experience, being female is tied up inexorably in surviving a society and a world that hasn't been kind to me. That ignores my words because of who they're coming from. That calls me 'crazy' and 'bitchy' when I'm angry at this because it doesn't take me seriously. That decides my worth based on my attractiveness and my willingness to put on makeup and smile. That has hurt and abused me no matter what I do to please it.