I addressed the issue of power dynamics between first cousins, but I am talking to someone who thinks fourth cousin relationships should be banned. There just is not a higher likelihood of an improper power imbalance in a fourth cousin relationship than between a pair of randoms, absent some extremely unusual family structures. Again, do you even know any of your fourth cousins? I don't even know any of my second cousins! I could sit down, think about it, and tell you all my first cousins, but nothing more distant than that.

Edit: an arranged marriage doesn't become more problematic if the couple shares a set of great great great grandparents, that's... That is honestly a bizarre thing to say. It's the arranged aspect that is problematic, not a very distant relationship between the couple. The power dynamic of the couple you describe is not in the least affected by the fact that they are fourth cousins.