I'm not sure anyone gets let into that part of the Church of the Holy Sepulcher. They won't even let scientists preform X-Rays to see if Christ is even in the alleged grave at the bottom of the inner chamber.

Frankly, I wouldn't be surprised if plenty of politicians have gone to the main church (but not the inner part), and just not gotten their picture taken, or potentially photography may be prohibited.

For example, many politicians regularly go to church every week, and we normally don't see them get their pictures taken as part of their own congregation. That's one of the reasons the May 27th Antifa Riots in DC were so bad. They burned that historic church where tons of politicians actually normally go on Sundays.

And from an even more cynical position, I wouldn't be surprised if the church is less photogenic than the wall is. A close up picture of a face and a wall is actually a fairly powerful picture. The inside of the church might not be a very significant looking picture that can be used as a close-up of the face, unless you're doing this 'worm's-eye-view' picture of the ceiling

Then, I have to wonder, given how Israel governs access to these religious cites, if there are crazy rules about who, what, when, where, and how visitors can go to these cites, and for how long. It's also apparently going under some kind of renovation, I guess?

Walls, on the other hand, are pretty simple. Any part of the wall will do, and it's a wall, it's low maintenance. At least for a picture.