Ben, do you really think that the prime minister has the din of a melech? Even the most fanatical zionists don’t say that. They don’t make a bracha on Netanyahu.
A king must be annointed, too.
Anyways, the abarbanel does not advocate for that shitah in the gemara; you misread. And where is this supposed sdei chemed? The rambam clearly paskened not like that shitah, that if a messianic candidate dies, he is disqualified.