Including countries where honor killings (of women--it's always women; why not kill the men?) are still shockingly common.

How could this be?

Because there isn't one "Patriarchy" thing that is the root of all evil.

The reason I haven't given a definition of patriarchy--I suggested three earlier--is because most of the time I don't find it used in an internally-consistent way. You offered, in all caps, "male-dominated dominance hierarchy systems".

But these have eight orders of magnitude differences in scale (e.g. all China vs. a family in Tunisia), several thousand-fold differences in frequency of violence (e.g. Sinaloa Cartel vs. Japan), and everything from girls being prevented from accessing education through to girls exceeding boys educational achievements overall while still having girl-specific efforts to improve their educational opportunities in areas they're not yet at parity in (e.g. Afghanistan vs. U.S. "girls in STEM"-type initiatives).

There isn't just one thing going on, and lumping everything together and calling it "patriarchy" isn't helpful except in gender-tribe internet warfare.

Violence-based hegemonic dominance is predominantly male, with rare exceptions. At the most extreme end, compliance is obtained largely by fear save perhaps for a small (sufficiently powerful) group around the leader. You can find numerous examples of this type of thing throughout history and in modern times--gangs are one example; the exploits of the Comanche are another. This kind of thing is grotesquely awful when it arises, and it is an ever-present danger. The murder rate among members of the Sinaloa Cartel can reach up to about 5% per year, due largely to fighting with other cartels. This is fully ten thousand times higher than the murder rate in Japan.

The Sinaloa Cartel isn't there because the "Man Box" attitudes--a reasonable proxy for Manosphere attitudes--are vastly stronger in Mexico than in the United States. They're comparable (https://www.equimundo.org/resources/man-box-study-young-man-us-uk-mexico/). No, the Sinaloa Cartel is as violent as it is because it is the dominant power in the areas it controls; nobody can stop it from abusing its power, and it has no reason not to abuse its power. Human rights, laws, impartial justice--none of that needs to apply. This violence-based hegemony would not be unfamiliar to the Assyrians; while a bit extreme, this is the threat that the largely (probably) more egalitarian hunter-gatherers had to, and could not, contend with historically. You could call this "patriarchy," even though there are a few women in positions of power among the Sinaloa (e.g. Sandra Ávila Beltrán: https://www.theguardian.com/society/2016/may/16/mexico-drug-cartels-famous-female-leader-sandra-avila).

At the other extreme, Japan, perhaps the most male-centric of all economically modern countries on the planet, also has the lowest murder rate. Everyone, especially young men, are deeply, deeply enmeshed in society. When young men do let their emotions get the better of them, highly-trained police use a variety of nonlethal methods to subdue the offender, ranging from judo to wrapping the fellow in a futon. Japan's homegrown organized crime syndicate, the Yakuza, is similarly almost entirely peaceful. And yet, all this is in the face of ubiquitous hierarchy, where men are systematically on top everywhere all the time. Only 11% of the members of Japan's House of Representatives are women, in contrast to 29% in the United States. You could call this "patriarchy" too, and it's way stronger in Japan than in the U.S..

But this patriarchy and the Sinaloa patriarchy have practically nothing in common with each other save maleness. Indeed, the kind of intense social knit throughout the entire country includes young men who are most prone to violence and is an immensely powerful inhibitor of anything remotely like the Sinaloa.

The best solution on the planet to patriarchy(Sinaloa) is patriarchy(Japan). It's true that the Nordic countries come close, but it's not true that the murder-level violence problem is a direct consequence of every type of patriarchy.

But there are serious problems with the male-centrism of Japan. Murder just isn't one of them.

So we have a bunch of things to consider.

We have to consider to what extent society is bound by law and custom and to what extent it is might-makes-right.

We also have to consider to what extent society is hierarchical and to what extent it is flat or heterarchical.

And we also have to consider to what extent society is egalitarian and to what extent it is differentially-assigned-roles (and consider that we might get different answers in different spheres of life--Americans are totally comfortable with female doctors but not female leaders; Pakistanis are more the other way around).

Using the term "patriarchy" indiscriminately to mean any and all of these presents an awful mess of conflation and self-contradiction, which is wonderful fodder for the Manosphere influencers who will gleefully point out that the only way this makes any sense is if the speaker is on an anti-man crusade. And people who are inclined towards problematic behavior are also likely to pay a lot more attention to that obvious hostility than the guy trying to explain that "no, well, you're actually being oppressed by a patriarchal dominance hierarchy system (just don't ask me to define what this means)" and "something something 35% better ROI for tech companies".

I think we can do considerably better, but I think we can also do vastly worse, and that a lot of the improvements are tricky, and that we need precise language and thoughtful appreciation for what is working well and what is poorly and to what extent.

Political examples of the authority gap are poor because in politics people use every frickin' thing to win. Trump berated McCain for being taken prisoner, for goodness' sake! People made fun of Boris Johnson's hair. Nobody cares about men's hair...unless they're in politics.

In business, again, the very top is a weird and ugly place. (We need to do a lot to make the tops of things less weird and ugly. This is not a patriarchy problem, but that's another long story.) But in most of society, people are pretty fine with women in authority. From 2014, most men are fine with whoever as a boss; women care more (and favor men by 14 points): https://www.linkedin.com/pulse/20141209154708-151385-do-you-want-a-male-or-female-boss-and-why/.

Anyway, problems? Yes. More at the top? Yes. Patriarchy? Not a useful term to use for most of the things you've complained about, but it is for some (like how Ms. Gillard was treated).

But the whole attitude that almost nothing has been done is silly--you present evidence against it yourself with the Pakistan vs UK numbers, among many other things.