Personally, I see no benefit in praying at the wailing wall, unless one had a somewhat preoccupied bend towards the idea of alleged holy physical places, which I think went out with the Old Covenant.
Hebrews 9:1 shows the Old Covenant system had worldly sanctuaries. Not the new. And I am not interested in wearing any religious garment in order to pray at a place required by those who are non-Christian in order to pray at certain geographical places. ...whether to display a cool photo or not. It won't enhance my prayers. But, like Barb says, if someone wishes to do so, then knock yourself out.

No biggie.
My thoughts, anyway.