Stricly speaking the Western Wall is the retaining wall that supported the wall that went around Herod's Temple. That site was razed to ground and saled down by the Romans so nothing might grow thare. We wroshp there by default on account of Halachic reservations about going "up the Temple Mount", though there are some opinons that say Maiimonides did reach the remnents of the Temple Walls when he was in Jerusalem. After '87, there were some Isreali intellectuals that weren't as enthusiastic about the Western Wall whatsoever, among them , Yishaiyahu Leibowitz , who created a stir over a public statement that it was hardly holy, at all.. As other talkbackers state, it seems that some non-Halachic Jewish leaders, for whom Torah and Mitzvot are a matter of "history", want to be part of this whatever, so .. . . . instead of taking what has been alloted for those Jews who do not subscribe to Halacha, and pray at the "Western Wall abd want equality over a wall that has fours sides, a Westrn side a Sounhrn side, a . ... and so forth and so on.
17-year-old Palestinian killed by IDF on Friday laid to rest near Ramallah (Haaretz)
from the article: Women praying at the wall: A question of the sun and the moon