No Palm Trees in Jerusalem?

It is sometimes claimed that there were no palm trees in Jerusalem. This would count against the reliability of the Gospels, as the Gospel of John specifically reports that Jesus' triumphal entry was celebrated with the waving of palm branches (cf. John 12.12-13). While this objection is uncommon and neglected by most skeptics, it is nonetheless present and deserving of a reply. 

We have extrabiblical sources which report the presence of palm trees in Jerusalem. For example, after Simon the Maccabee expunged the Syrian forces from Jerusalem, we read in 1 Maccabees 13.51 (CEB): "On the twenty-third day of the second month, in the year 171, the Jews entered it with praise and palm branches, with harps and cymbals and stringed instruments, and with hymns and songs. A great enemy had been crushed and removed from Israel." 2 Maccabees 10.7 (CEB), chronicling the same event, says "So they held ivy wands, beautiful branches, and also palm leaves, and offered hymns to the one who had made the purification of his own temple possible."

And from the Bible itself, Nehemiah 8.15 (CSB) says "So they proclaimed and spread this news throughout their towns and in Jerusalem, saying, 'Go out to the hill country and bring back branches of olive, wild olive, myrtle, palm, and other leafy trees to make shelters, just as it is written.'"

It's highly unlikely that all these comments about palm trees would exist if they didn't grow in and near Jerusalem.

D. A. Carson asserts, "There was little difficulty obtaining palm branches: date palms were plentiful around Jerusalem, and still grow there." (The Gospel According to John, 1991, p. 432). This can be seen in pictures of Jerusalem. See here, for instance.

The quotations from 1 Maccabees, 2 Maccabees, and Nehemiah, alongside the current existence of palm trees in Jerusalem, render this objection broadly untenable.