If your dense housing leads to higher housing costs that's actually great news; it means that your city is enabling higher-productivity arrangements that boost local incomes
Take Milan as a counterexample. A single room in a shared flat costs around €700/month, a single-room studio €1200/month. Yet, people on average earn €30,000 a year, which means €24000 after taxes, or around €1800 per month. That's not what I would say increased salaries and productivity.
In Italy, there are serious problems with stagnating productivity and national, collective bargaining. Nevertheless, that doesn't mean rents do not skyrocket in big cities
Take Milan as a counterexample. A single room in a shared flat costs around €700/month, a single-room studio €1200/month. Yet, people on average earn €30,000 a year, which means €24000 after taxes, or around €1800 per month. That's not what I would say increased salaries and productivity.
In Italy, there are serious problems with stagnating productivity and national, collective bargaining. Nevertheless, that doesn't mean rents do not skyrocket in big cities