Are you referring to this?
That's your evidence? Perhaps this is some spiritual proof, but we find:
a. When Saul and three of his sons were killed, Ishbosheth his fourth son was crowned and accepted by Israel as king.
b. Adonijah was accepted as king by several members of the government despite God already commanding that Solomon would be the rightful heir.
c. Solomon recognized Adonijah as a legitimate threat to his throne and had him killed.
d. Jehoram son of Jehoshaphat killed his brothers for the same reason.
The people of Judah had a lot of pull in terms of who was king and who wasn't. They crowned kings and dethroned them (see for example 2 Kings 11:14, 2 Kings 14:21, 2 Kings 21:24, 2 Kings 23:30). Perhaps you will try to differ to spiritual legitimacy, but we see that legal, mortal legitimacy was, in some cases, far stronger. So, I'm not going to have that as evidence for a differentiation between "natural descendants of David" and "royal descendants of David".
Perhaps you should try that some time, instead of telling others to do that.
I don't know who argues that, but I did notice that you completely ignored the last verse in Haggai, Haggai 2:23.
I recommend listening to what the scriptures do say and giving them some thought.
I don't know why you quoted these verses. Is it evidence against Zerubbabel, because his name wasn't צמח ""branch""? If so, then it's also evidence against Jesus.