It’s also worth noting an additional concept which is left out of most discussions:
Going up to har habayis is a question of kares.
We find that when dealing with kares, especially in areas where there is room to make mistakes, we go overboard to prevent the slightest chance.
Thus chometz on Pesach is prohibited b’mashehu, even the smallest amount, because consuming it incurs kares.
Likewise, we put tremendous safeguards in place when a woman is a nida, in order to prevent her and her husband from inadvertently stumbling on this severe prohibition.
And the Torah prohibited Yichud with a forbidden woman- one of the very few examples of a siyag min hatorah- because of the issur kares involved.
When we are dealing with a shailoh of kares, and it’s an issue which is given over to regular individuals (as opposed to specific gedolei yisrael who are known for bein yirei shomayim), the proper thing to do is be strict.
There’s no chiyuv to go up to har habayis, and it’s not even clear there is an advantage to going up (instead of just going to the kosel) without having a beis hamikdash to do avodah.
Most of the reasons I’ve seen for going up fall in to one of two categories:
1) emotional, poetic claims- “AH, how amazing it is to finally be back on top after 2000 years! You can feel the kedusha here!”
2) nationalistic claims- we need to assert our sovereignty over Har Habayis, and the way to do so is by going up
The first reason is nonsense. Poetry has no place in halacha. And emotional claims of “feeling” kedusha are made up. (Almost) nobody can truly ‘feel’ kedusha!
(There’s the famous story of the woman who came to Rav. J.B. Soloveitchik asking permission to start wearing a tallis. He told her that she shouldn’t just “jump” into the mitzvah; she should start wearing it without the strings for a while, and them come back to discuss if she is ready to put the strings on.
After a while she came back, and he asked her about her experience. She said “Rabbi, I can feel the holiness in the tallis. I’m truly ready to put the strings on!”
He answered her, “A tallis without the strings is nothing more than a shawl. If you can feel so much holiness wearing a simple shawl, you don’t need to start putting on tzitzis!”)
nationalistic claims are also problematic. Where do we find that we bend the halacha because “nationalism” plays a part?
(We do find cases where chazal permitted certain things, where not doing those things would result in Jews losing out on owning Eretz Yisrael. But here the status quo is not being challenged by the arabs; we’re not in danger of losing control of Har Habayis, in the sense that chazal talk about.)