First of all, it should be clear that Hajj is obligatory once in a lifetime. If a person has the means to perform Hajj, he should carry it out as soon as possible. One is not advised to delay performing Hajj under any pretext, keeping in mind the fact that Hajj is one of the pillars of Islam. The Prophet (peace and blessings be upon him) said, “Islam is built upon five pillars: testifying that there is no true god except Allah and that Muhammad is the Messenger of Allah, performing Prayer, paying the Zakah, making the pilgrimage to the Sacred House (Hajj), and fasting the month of Ramadan.” (Reported by Al-Bukhari)
As far as the question in point is concerned, we can say that it is not a requirement to climb Mount `Arafah. Standing at any place of `Arafah is sufficient and you are not required to climb the Mountain of Ar-Rahmah (Mercy).
In his well-known book, Fiqh As-Sunnah, the late Azharite scholar Sheikh Sayyed Sabiq states the following:
“A pilgrim may spend the Day of `Arafah anywhere within the bounds of `Arafah, for all of it is equally good for encamping (on this particular day) except the bottom of the valley called `Urnah to the west of `Arafah. There is consensus that spending the Day of `Arafah at `Urnah is not sufficient to fulfill the condition of staying at `Arafah. Spending time near the rocks or as close to them as possible is commended. The Prophet (peace and blessings be upon him) stopped at this place and said, “I have stopped here, but the whole of `Arafah is a stopping place (for the Day of `Arafah).” (Reported by Ahmad, Muslim, and Abu Dawud on the authority of Jabir)
Climbing the Mountain of Ar-Rahmah or the belief that standing on it is better than standing in any other place is wrong. Nor does doing so represent a Sunnah of the Prophet (peace and blessings be upon him).