This argument is simply not true, or at least not so general.
You can't say that so generally, I agree with you on that. Here in Dresden, the salaries in the city are definitely higher than in the more distant surrounding areas or in the Ore Mountains, but the rents are also somewhat higher. Often, one car is also unnecessary, whereas in the countryside/small town you rely on 2 cars.
Large industrial companies in rural regions do not pay significantly less either in the collectively agreed or in the non-tariff sector.
However, the majority of the population is not employed in large industrial companies or corporations but in the middle class, and different salaries are paid there than in corporations.
Finally, a question: Do you believe that an engineer at Daimler or BMW earns three times as much as at VW?
Do you believe you have three times higher monthly costs than others? That might apply to rent or costs for land, but there is much more than that. Additional rental costs, gasoline, vehicle taxes, insurance, comparable clothing, comparable food, purchase of vehicles/white/brown goods – that is, all daily necessities cost about the same for you as in the remotest corner of Meck-Pomm. The major price differences are probably mainly in the service sector.
I do not complain that less is paid here, because we deliberately moved to the Dresden region and not to the old federal states and we also want to consciously work for the middle class and not in a corporation. On the other hand, I find it presumptuous to complain about the costs if you want to work in Stuttgart or Munich and simply ignore the positive facts.