You're trying to take a specific situation (inflation caused by government spending focused on job creation and improving the lives of the people) and apply it to a completely unrelated situation. Wage stagnation is a 40-years-and-running issue created by policies pushed by the same wealthy people who are pushing the austerity and anti-inflation agenda that you're co-signing. In fact, our periods of recession have exacerbated that wage stagnation the most. By your logic, the middle class would have been better off if the government didn't print stimulus checks and extend unemployment, which is ridiculous.But that hasn't been the case in the past 10-15 years. Wages have not kept up with inflation and people are getting by tapping into more debt. Outside of falling purchasing power (the dollar isn't stretching as it used to), there is still the issue of rising government debt which will get much more expensive once the Fed raises rates (they will do it eventually, especially as inflation starts to pick up). Once that happens the government will have to raise taxes which becomes a double whammy for the populace (high inflation/falling purchasing power and increased taxes).
The government has a mandate to ensure its citizens have the opportunity to pursue a better life, but there has to be a measure of sustainability with spending. If it's increasing Corp taxes or cutting the defense budget in part to fund it I think that's good. But the lasagna approach of layering is irresponsible. The bill will come due and when it does, it's the citizens that will suffer.
Like I said, look at who is pushing your austerity agenda. That should be all you need to tell you who really benefits. In fact, look also at the people who are pushing your "But we can't do government spending because inflation hurts the common man!" claims. You'll find that those arguments are not sourced from the people who typically give a shyt about the common man.