America (Loyalists were a minority in the American Revolution), Italy and Greece beg to differ. You can add post-Second Empire France as well.
Monarchism is and has been a fringe for a long time in all major non-monarchical states.
Greece was under the control of a military junta that wanted king Constantine gone, a referendum doesn't give you much of a choice when a man with a gun is breathing down your neck. With Italy, I've heard the referendum may have been rigged, but I haven't seen enough evidence to say for certain. Iceland is the only other one that can be attributed to popular cause, but given the country was occupied by the US at the time, I can't help but be a little suspicious.
And those examples don't detract from the rest, I said
almost so we still have Brazil, both Mexican Empires, the Second Haitian Empire, Barbados (where republican politicans admitted they wouldn't hold a referendum because they knew it would fail), Guyana, Portugal, Spain's two republican experiments, France's Ancien Regime, the English civil war, Germany, Austria, Poland, Finland, Lithuania, Russia, Ukraine, Romania, Bulgaria, Yugoslavia, Montenegro, Albania (where a failed restoration referendum was
admitted to be rigged), Turkey, Iraq, Yemen, Egypt, Libya, Ethiopia, Rwanda, Burundi, South Africa, Mauritius, Iran, Afghanistan (where a restoration was very much wanted, but vetoed by the US occupation administration), Pakistan, Sri Lanka, Maldives, Nepal, China, Laos, Vietnam, Cambodia's absolute disaster of a republican period, the other former commonwealth realms, and that's not even touching on cases like Sarawak, Sikkim, and Hawaii where the country itself no longer exists.
Now as for your second point, polls in Georgia show an increase no matter how you slice it, with 2003 saying 45% yes and 30% no to a restoration, and polls in 2013 at 79% at most and 56.8% at lowest in favor of restoration. A 2017 survey in Russia saw support at 37%, a 2015 poll in Serbia gave restoration a 49% approval, up from 39% in 2013. In Romania, 21% in 2016, 37% in 2018. And if it was so fringe, then why have, as previously mentioned, Montenegro and Burundi already taken steps to restoration? Why are protesters in Iran rallying around the crown prince and why are Libyans carrying around portraits of Idris I? These people know republicanism has failed, the rose colored glasses that politicians promote by putting the ideas of democracy on a pedestal as this unquestionable supreme virtue are falling off and they're looking for something better, something that won't force politics into every aspect of their life, something that won't be more concerned with ideological purity than simple pragmatism, something that will foster unity instead of division. They're realizing that political power is not a blessing for all to enjoy, it's a soul-crushing burden that is best left to those who are equipped and trained to handle it. Republicanism is totally incompatible with these simple needs for peace and happiness, it thrives off the collapse of social harmony because it makes it easier for the political class to abuse tensions, it's a vicious cycle of manipulation.
People are slowly but surely finally realizing what people like Hobbes, Plato, and Kuehnelt-Leddihn knew all along and have been saying for millennia. This idealistic notion of total political egalitarianism as the perfect state, a nice thought though it may be, is ultimately unrealistic and doomed to destroy itself by fetishization of unnecessary conflict, extensive politicization creating resentment and division, and what I can only call ideological brinksmanship pushing polarization and extremism that can only end in either tyrannical dictatorship or political collapse. It's no surprise more and more people are turning to the only real alternative. The death of republicanism is inevitable because it's a system that slowly destroys itself, whether that takes a few years like Afghanistan or hundreds like the USA. A country cannot survive with it's only leaders being these egotists who's only real skills are in speaking well enough to trick people into liking them and telling them anything other than them is the root of all evil. Sooner or later that's gonna break.
EDIT: only just now realizing I probably shouldn't give a monarchist filibuster in a simple what-if thread. I got carried away and defensive. gonna leave everything here since I may as well, I'm not gonna pretend I didn't say it to try and save face, but I promise I won't go on any more tangents in this thread and keep any future replies to the subject of hypothetical post-soviet monarchies. Apologies for the digression, everyone.