You make many interesting points, and I accept nearly all of them. On addition, I'd note that one of the ways that absolute monarchies provide more stability is their long-termist nature compared to democracy which must have its officials tied down by a time-limited mandate. Short-termism is a institutional problem for democracy in that it causes officials to prioritise appealing to immediate to short-term goals and objectives, even if they have long-term negative effects, in order to ensure that they can maintain the popularity to continue to hold their office. This also prevents the constant changes in the direction of the state due to changing governments and popular opinion. I remember reading a quote that sums this up, which I forgot the exact details and author of, which went a long the lines of "democracy is a constant cycles of revolutions and counter-revolutions". One decade you will have a government that does X, then you'll have a government that does Y and messes up all what the previous government worked to do in just two years. Obviously, such an erratic nature always causes fluctuations in the living standards and the prosperity of the nation.

However, I do believe that monarchy has some problems which makes it inferior to other absolutist and dictatorial systems. Firstly, in terms of hereditary monarchies, while they do admittedly provide a generally-more stable system of succession than some others by usually having pre-determined orders of succession they have flaws in my opinion.

• The reliance of the system on the sexual success of the head of state, meaning if they fail to heir a progeny, then the succession becomes complicated and there can be a succession crisis between siblings of the monarch once he dies. And if there is neither progeny nor siblings, the state then has to go find another monarch which can itself cause problems.
• Succession to children and other incapacitated individuals, when this occurs the state effectively goes into a period of regency which can cause disruption in terms of governance.
• Potentially dysgenic nature due to rule being based on lineage not merit.

I do think one benefit of hereditary monarchy though is that the nation is treated as the property of the ruling family, thus there is some self-interest commitment for them to at least govern it adequately to ensure that their own offspring can continue to rule it.

In contrast, there are elective monarchies (I know some people dispute whether these were actually monarchies). The most notable elective monarchies in Europe are Rome, the Holy Roman Empire, the Papal States/Vatican City and the Polish-Lithuanian Commonwealth. I do believe that elective monarchies ala Rome are superior to hereditary monarchies because succession is not constrained by lineage from a single family, meaning that transfers of power can be done based on merit (although not always the case). However, a problem with these are that the electors (such as the nobles of the PL Commonwealth or the Roman Senate) often possess a disproportionate amount of influence and that can in itself cause political instability. Only the Papal States were relatively immune from internal issues due to the religious nature of the highest office (although there were still disputes, eg. antipopes).

While I believe in a more absolutist state, I do not see the outright advantage of a monarchy over any other kind of autocratic government such as a modern one-party state or a military junta (which have their own flaws). A president-for-life can basicially do all that a monarch can do. While there is a traditionalist argument for monarchy on it being a cultural institution as well, I don't think it would be that persuasive in the modern era (I'll address that in the next parapraph). I think states like modern China or the Islamic Republic of Iran provide better models for a more meritocratic government whereby officials work their way up the power-ladder would be better. I especially admire the Imperial exam system of ancient China, I think something like this could be used not just for civil servants but for public officials (albeit I would want testing to be very philosphically and physically rigorous).

Finally, in terms of the modern applicability of monarchy as I said I was going to talk about last, the reason I do not believe it is suitable is because I don't see their being much appetite for monarchy in the West. Historically, monarchs governed based on the divine right from God or as vice-regents appointed by God's will. Such excuses are obviously not as convincing in largely modern secular societies, and I think even if people moved towards social conservatism they would still be quite secular in terms of their cosmological views. I could only see a monarchy really ever returning following the rule of a "Great Man"-esque figure who would decide to establish some sort of hereditary rule. In the West today, monarchies only really continue to exist as bizarre, glorified celebrities and people are mostly apathetic to them.