That's already happening. IMHO you have the causality backwards - prices started rising in 2020, and then some workers have captured some of that surplus by switching jobs, and now landlords are trying to capture the workers' surplus by raising rents. Rents follow wages, which follow profits, which follow prices, and then prices follow rents & wages again in the wage/price spiral. Homeowners have an advantage because their biggest cost of living is fixed, while rents generally rise to capture all available wage surplus.
The folks who really get screwed are the ones with fixed incomes but variable expenses, either a renting retiree or someone who plans to stay at the same employer for a lifetime. You should be aggressively changing jobs and going where the money is to capture some of the large amounts of money that are floating around. People who do that usually do better than average.
Note that while this is happening bad things happen. It often is the case that you have to live on less real purchases for a few months until your wages go up. However as a homeowner the mortgage not changing means it only takes one or two rounds to get ahead of this forever (that is before you never revert to worse than when you bought the house - you can go backward in purchasing power but not that much), while as a renter your rent will increase yearly and that is often a big hit against your wages that won't increase at the same time (and often not at the same rate - it will balance out in 5 year but that is a long time to live)
Don't read the above as a rant against renting. There are other pros of renting. You need to make the right decision for your personal situation.
If only retirees, and highly paid professionals are shielded from housing increases I’d expect all other prices to become correlated with housing as workers demand commensurate wage increases or start refusing to work for negative earnings.