When inflation goes unchecked, as it has in many other countries, wages go up at the same rate as prices. Unchecked inflation means everything goes up at once. Even here, wages have been going up.
You are confusing the cure and disease. If wages increase more slowly than inflation, it’s because there are policies aimed at keeping them down. Those policies are an attempt to control inflation throughout the economy.
Finally, inflation doesn’t “let” anyone raise prices, it’s a measure of how much they have already raised prices. And it doesn’t “recoup” anything, because investors care about inflation-adjusted gains not nominal gains.