You are not understanding that the economy is connected. It is not just that worker or that burger. When the minimum goes up, people making more than the minimum will get more, too. Many union contracts are pegged to the minimum wage. They automatically get raises if the minimum goes up. They could already be make 2-3x the minimum, but the contracts move them up. Even in nonunion environments, if you want to keep your good employees happy, when the minimum goes up, so does everything else. You cannot claim moral high ground based on intentions. I am sure that you and many others truly believe that boosting minimum wages will benefit the poor. The data shows just the opposite. Sure, for a few weeks or months, those who keep their jobs will have a bit more.
It is super scary right now because we have money supply concerns on top of pressure for massive increases in the minimum.
The money supply is the cause of inflation, though no CPI measures it. Inflation in the last few decades has attacked the basic means of social advancement. When I went to college in the '60s, I think tuition was $325/term, and a dorm room with 3 meals a day in the cafeteria was $365. Work-study paid $7/hour for washing test tubes, plus extra credit for making 1 molar standard solutions. I got $50/month from the Army as long as I was enrolled full time. At 10 hours a week working, I could cover one term of college with two months income with enough left over to buy records, meals out, movies, and hobbies. Try that today.
Fifty years ago, the primary means of wealth generation was home ownership. Even weekend warriors could get a 5% assumable VA mortgage. You could spin just about any paycheck into home ownership if you didn't drink it away. At the root of it, that's what the MAGA folks are really talking about. Inflation took that away, and it's not the price of a can of pork and beans that took it away, it was the printing presses and the vast accumulation of wealth that pushed basic assets like home ownership out of the reach of someone starting out. If you can't buy a house in your 20s, how are you supposed to get married and start a family? I know several young people who have resigned themselves to never owning a home, even though they want to, because of asset inflation. Call it sticker shock.
Superficial metrics like the CPI-U or the CPI-W are relevant to retired people because we have already garnered our assets. We own our homes, cars, tractors, and furniture. Maybe we even bought stocks when they were 10% of current prices. We could pretty much snooze through life and still end up with a decent nest egg. The only big inflation indicator we have to deal with is medical insurance, and that is mostly covered by Medicare. That level of economic security was not destroyed by hotel maids and burger flippers, it was destroyed by a system that left them sucking hind teat while vast accumulations of capital pushed asset inflation to extreme levels.
Yes, an increase in base wages would trigger an increase in the CPI. It would have little effect on inflation as a whole. To correct that, we need to shut off the printing presses and go through a period of high asset deflation. The oligarchs would bring down civilization first.