What you're saying here is that you want to prioritise your way of enjoying the monument over their way of enjoying the monument. Nobody has a right to do that. They have as much right to be there enjoying the monument in their own way as you or I have. There's no rule, written or unwritten, that says people should move along quickly leaving the place clear for photographs and for people who prefer tranquillity.
I say all this with the greatest sympathy. Cyclists turned up when I was at Wayland's earlier this year and I was infuriated and wanted to do unpleasant things to them. But I have to recognise that this is my problem and not theirs, so I waited patiently for 15 mins until I could get clear photographs. And if they'd stayed longer, I'd have been really frustrated, but.... still my problem and not theirs. Maybe some people get wound up by photographers prowling round taking photos and making them feel unwelcome and awkward?