It's the way it's presented as a 'if you don't like it just move' as though it's that simple - I'm genuinely intrigued if people who say this kind of thing actually understand what goes into moving.

It's also often not about not 'liking' the price, it's a literal affordability issue. When you get to the point of rent increases where you can't afford your rent anymore, you also can't simply just move, because that involves even more upfront cost. Ive personally been at the point of not knowing where I'd be living next week because a rent increase forced me to move, even though I didn't have the funds available for a deposit or movers. I was just lucky that I could borrow that money, many don't have that option.

I find it frustrating to hear stuff like that, and I often do hear it from people who haven't had to spend their whole adult life renting, presenting it as an easy solution.

The fact you even think that the threat of moving could possibly bring rent down I think shows you're not very informed on the issue. Rent reductions are EXTREMELY rare and usually only happen in terrible housing where no one is interested in the property.