The problem with this logic is that you need to argue the reverse too: that reducing inflation would be best done by taxing people so they can't spend as much money.
There's no inherent need to do any such thing. In fact, there are multiple problems with this -- raising taxes doesn't reduce the velocity of money unless the government is just going to sit on it, otherwise it does exactly the opposite as it will increase government spending. Recall earlier I mentioned the velocity of money, read more about it here:
https://ancillary-proxy.atarimworker.io?url=https%3A%2F%2Fwww.investopedia.com%2Ft...
Notice the mention of GDP. Riddle me this: What factors into GDP?
A far more effective way of slowing inflation is raising the interest rate, which encourages everybody to save rather than spend. And guess what? That's exactly what central banks do -- raise interest rates, not taxes.
That very clearly shows the flaw in the logic.
No, it very much does not. In fact, saying that anything "needs" to be argued is just another form of begging the question, which is another way of saying that you're reaching a conclusion before the argument, which is a logical error. And as I just explained, not coincidentally, you reached a very false conclusion.
The truth is that inflation only marginally rises with increased income
This is true, but you're missing another point that I already made. Yes, you see an acute increase in prices each time the minimum wage increases, but not quite at an amount to match the wage increase. For every 10% that you raise the minimum wage, food prices see a short-term increase by 4%, and everything else is generally around 0.4%. So if you think about that in terms of food, then for every dollar extra you got from your minimum wage increase, you're now spending an extra 44 cents, meaning you effectively got a 66 cent wage increase. But remember, these increases hit everybody, not just the minimum wage earners, which brings me to my earlier point...
so there is a net increase in purchase power
This is false. It's temporary at best, and only for the lowest wage earners, which is why I say it never feels like "enough". The median income varies over time, but it's generally significantly higher than minimum wage, which means most people earn more than minimum wage. In your mind, you're thinking you're taking money away from the rich and giving it to the lowest income earners, but you're really not. Those percentage figures I gave you earlier are a percentage of income increases for those AT minimum wage. The higher in incomes you go, the more meaningless that increase is, and the fewer people even pay that increase overall. In Marxian terms one might call "lower middle class" is the one bearing the brunt of this. Essentially, their collective purchasing power decreases to a higher amount relative to those at the bottom, because as you know, they didn't get a pay increase.
So suppose we had a minimum wage of $10, and you're making $11. A bill passes to raise the minimum wage to $11. Minimum wage earners, over the next year or so, see an effective 66 cent pay increase. Meanwhile, over the same period, you and a lot more people get a reduction in pay of 44 cents. Yes, this is using some incredibly oversimplified math and assumptions, but the gist of it remains.
The net effect of that is just a wash. I've had almost exactly this happens to me before, by the way, in my early 20s. I was kind of annoyed by it because I had more technical skills, hence I was paid above minimum wage, unlike most of my coworkers.
That is nonsense as it assumes that all additional income is spent and that all that spending converts directly into price hikes of things they buy.
Then go argue against data.
https://ancillary-proxy.atarimworker.io?url=https%3A%2F%2Fdocs.iza.org%2Fdp1072.pd...
Let me know how that works out for you.