In the "short" term sure (the next few decades-centuries), but in the long term, it is noteworthy that the number of absolute monarchies among the Great Powers consistently declined throughout the 19th century, ultimately becoming extinct by the end of World War I. While a Liberal-Democratic Republic or Westminster-style parliamentary monarchy aren't the only alternatives to absolutism, the dominant political systems of the 20th and 21st centuries (including non-democratic ones like one-party states) share some key attributes which are fundamentally at odds with the principles of a traditional monarchy.
- National Identity: Perhaps THE distinction between modern and pre-modern states is the emergence of secular national identity that transcends personal or dynastic loyalty and religious affiliation.
- Popular Sovereignty: Deeply connected to national identity, modern states place tremendous importance on the concept of popular sovereignty, which asserts that the power of the state is derived from the consent of its people. This is true even in modern autocracies, particularly in the most successful ones like the USSR or PRC, (or for a non-Marxist-Leninist example, Singapore) where tremendous emphasis was/is placed on obtaining at least the illusion of popular support, if not the genuine article.
- Rule of Law: Finally, at least on paper, modern states claim to have a fair and impartial legal system to which all citizens are accountable. To what extent this is actually the case varies over time and between countries, but generally speaking, nations that are better at fulfilling this ideal are more stable and MUCH more economically prosperous.
One cannot easily reconcile these features of modern, developed countries with a hereditary head of state and government claiming legitimacy as the vicegerent of God. At best, such a system evolves into one where the continued existence of the monarchy is legitimized purely by economic performance, as seen in Saudi Arabia and some of the other gulf states, or one where the monarchy is so marginalized as a political force that its abolition isn’t worth the trouble, as in many European countries. In either scenario, the position is precarious, and does not lend the monarchy any inherent legitimacy beyond the persona of the monarch.
Thus, at least in my opinion, the best option for Rhomania is for Konon's idea of non-hereditary transfer of power to win out in the long run, alongside a revitalization of the senate into a functioning legislature, and the establishment of formalized rules for succession-the closest thing they have is the idea that the emperor is acclaimed by the senate, so make that official-and give the senate the ability to recall/dismiss a serving executive. That retains the unique feature of a monarch (or "monarch") with actual political power without condemning Rhomania to the kind of extractive kleptocracy seen in 21st century absolute monarchies.
Being a 2,132 year old institution didn't spare the Chinese monarchy from being stamped out in a matter of years. Without adapting to modernity (and crucially, articulating a coherent claim to legitimacy in modern times apart from simple performance or the personal popularity of the monarch), the Roman monarchy is likewise doomed to be marginalized, removed by force, or end up dragging the nation down with it.