Islam critiqued doesnt know for sure; Becca in Psalms?

In answer to the video "Abraham and the Kaaba: From Borrowed Stories to Sacred Scripture"

In Psalms84, David speaks in his prayers to the Lord of hosts -the Lord of all nations-, of pilgrims frequently going through the valley of Beca to pray at the altar. Some attribute this psalm to David, others to Korah's 3 sons who lived in Moses' time. Jewish oral tradition states that the book is entirely David's who took the earlier works and melded them with his own ideas. In that passage Becca is identified by a definite article meaning a specific place. That place could not be the Jerusalem Temple, which was not even constructed at the time (neither in Moses' time).

Of course, later in Jewish history Zion became affiliated with Jerusalem, but it couldnt have been during the time of David, or Moses for that matter. Jerusalem in the sense of the Holy City and place of pilgrimage was not built yet in David's days who was in addition referring to a place far away that required strenuous effort. The context of Ps84 is that of difficulty as one engages in a dry and barren valley then gaining spiritual strength upon strength. Clearly the meaning as noted by all commentators cannot be anything than the "valley of lamentation/weeping". The root word, bacca is used for types of trees that grow in arid places, like balsam, mulberry, or aspen that drip resin like tears. The balsam tree itself is found in southern Arabia, as well as on the mountains of Mecca and Medina.

So then which valley in Jerusalem is the ground so hard that the rain collects in pools? The valley of Becca has this particularity and the passage is meant to demonstrate its aridity. A valley of trees and lush vegetation doesnt fit this description. Which valley in or around Jerusalem do people take rest in and make it a well, when they go through to "Zion"? The fact that they make it a well, show that they take their rest there as well, another specificity of the place.

David laments that this place is far from the people and much hardship has to be taken to get there and despite the hardship, as they proceed to it and get closer to the court of the Lord in 'Zion", they move with strength upon strength. So where is that arid valley that pilgrims ever took on their way to Zion?

None of this was applicable to Jerusalem, nor is any valley affiliated with the pilgrimage to Jerusalem, besides the fact that the Temple didnt even exist then.

David speaks of Becca as a frequently journeyed site by pilgrims and there was no place in his days nor before, to the point that certain commentators argue that what David is referring to is a place in heaven. This is ruled out by the fact it is refered to as a geographical location which Bible scholars have not been able to identify until now. Since pre-islamic times, Arabs identified Mecca originally as Becca as corroborated in the Quran.

One of the BEcca's defining characteristics, per the Psalms is that rain collects in pools when it rains because of the hardness of the grounds, which isnt Jerusalem's case, besides the fact that people journey to it through valleys

"Who passing through the valley of Baca make it a well; the rain also filleth the pools".

Mecca is enclosed between valleys and Jerusalem, which is on a small range of mountain tops in no way can be said to fulfill these qualities. The Zamzam well is what made the location hospitable to the pilgrims. This is where the HB states that God openned Hagar's eyes to a well, in answer to her supplications

Gen21:18-9"Arise, lift up the lad, and hold him in thine hand; for I will make him a great nation. Then God opened her eyes and she saw a well of water. So she went and filled the skin with water and gave the boy a drink".

This was God's gift to her, a means of sustenance for her settlement there in accordance with His plan and promise to make a great nation out of Ismail. As a side note, none of the wells of Beerseba or anywhere near it are mentionned as God-given. They are very distinctly described as the work of human hand. Nor is there any local tradition pointing to the existence there, now or in the past, of any divinely caused well. The only well made to gush miraculously in connection to Hagar and Ismail is in Mecca.

It is interesting to note also that by the time of the great rabbinic scholar and Torah commentator ibn Ezra, when every historian and religious scholarly authority agreed that the inhabitants of hijaz are descendants of Ishmael, he comments that the well which Hagar was miraculously pointed to prior to Ishmael's birth in Gen16:14 was originally called Beer Lahai, meaning 

"the well of him who will be alive next year..The well was so called because the Ishmaelites held annual festivities at this well. It is still in existence and is called the well of zamum". 

This well, present in his time and known accross cultures, is mispronounced as Zamum. Obviously no other well than that of Zamzam exists, where Ishmaelites ever held festivities prior to Islam.

Some Bible versions say "Valley of Tears/ Weeping", and Beca means "crying" in Arabic as a reference to Hagar crying for Allah's help in the wilderness fearing for her son Ismail's life, as related in both the Torah and Islamic tradition.