No, monarchy as a serious way of running modern countries went out of fashion because it did not work well, and too many of the members of the various royal families of Europe were at best incompetent, if well-meaning.
Even the less impressive royals could hardly do worse than the current crop of European politicians.
Assuming that Europe's rejection of monarchy refutes monarchism is as illogical as it would be to assume that Europe's rejection of Christianity refutes Christianity.
Maybe the West can have a look at what happened to each Chinese dynasty: each time a dynasty replaced the next, it had always been an overthrowing as the successor claimed each previous dynasty had "lost the mandate of heaven". You can have:
1) Vassal state overthrowing the previous dyansty: Shang Tang overthrrew Xia dynasty and founded the Shang dynasty in 1751 BC. In Chinese history texts they are called "Nobility revolutions".
2) Peasant rebellion and taking the throne himself: Liu Bang did this to the Qin dynasty in 206 BC and founded the Han dynasty (one of the most glorious Chinese dynasties), and Zhu Yuanzhang over threw the Mongol Yuan dynasty in AD 1386 and founded the Ming dynasty. They are called "Peasant revolutions" in Chinese history.
3) In-laws taking over the thronw: Yang Jian overthrew his son-in-law's throne in Northern Zhou and founded the Sui dyansty in AD 581.
4) Generals taking over the emperor in a coup: Li Yuan did this to Sui dynasty in 618 AD and founded the Tang dyansty, Zhu Wen did this to the Tang in AD 907, Zhao Kuangyin plotted a coup and became the first emperor of the Sung dynasty in 960 AD.
5) Foreign invasion: the Yuan and Qing dynasties conquered China.
It may give a better chance of getting a competent ruler on the throne, because you get to throw the bums out once every 200 to 300 years. How about allowing this in Europe?