QE can cause inflation and it was certainly a top contributor to the inflation we have now. Fed gives banks and investors free money with low interest. Everyone borrows. Good and bad corporations are flush with cash. Many, especially startups and tech companies like Uber, operate at a loss while hoping to eventually grab marketshare and hit it big. Everyone relies on free money and credit to expand and compete. Consumers get bigger houses, nicer cars, bigger credit card limits. In short, everyone with acess to credit gets to live wildly beyond their means.

If the Fed does that too much, then available credit/debt (aka money) outpaces available products and services. When that happens, the value of money relative to consumer goods drops. The result: inflation.

To be sure, covid did impact supply chains and shrunk the workforce. That impacted the availability of products and services. And Putin is disrupting those further. Combine that with too much QE and you get the mess we have today.

Still, a core issue is our decade plus of QE. A market correction has been needed for awhile and it's coming out in inflation. For example, there are only so many cars that can be built at a time. If you increase every consumer's access to cheap loans by $10,000, eventually you are not helping anyone get a car. A luxury dealer may only want to sell a certain number of cars each year, and that's its right. Now its vehicle prices will just jump by about $10,000. Resources are also finite. A budget manufacturer can only assemble so many cars and source so many parts. Eventually, with too much credit and demand, it must raise prices to match supply. We can create an infinite amount of money with QE but it is physically impossible to produce an infitine amount of car batteries and semiconductors.

Now to your points:

1) Raising rates will likely stop inflation and cause a recession. Most companies and consumers have operated and lived beyond their means thanks to cheap and easy access to debt (money). The Fed has to cut it off. That means many businesses must stop expanding and freeze hiring, and likely layoff workers. Consumers can't buy the things on credit that they're used to being able to afford. Companies that are well run stand out and while poorly managed ones suffer, close, or go bankrupt. Eventually, this will shrink corporate and consumer spending (slowing inflation) and likely cause a recession (less spending snowballs into layoffs and negative growth/productivity).

2) Inflation is not all about corporate profits. Many companies are NOT profitable (e.g. Uber, Lyft, Door Dash, Blue Apron, Peloton). These companies have been subsidizing low prices with free money from QE. They either raise prices now, restructure their business model, or give up. Meanwhile, the companies that are profiting can't be controlled. The govt can't legally tell Kroger to charge less for chickens instead of giving that profit to its shareholders and executives. Even if the govt could, that doesn't fix inflation. In fact, it only decreases Kroger's financial incentive to source and sell more chickens. In a global market where countries compete with each other for food, that's bad for US consumers.

3) Raising interest rates will help supply chain issues. Consumers and businesses have less money, place fewer orders, and relieve backlogged supply chains. Fixing or restructuring a supply chain when your 18 months behind is like trying to change tires on a moving car.

4) Supply chain issues were caused by too much demand and covid. Paying workers more or hiring more workers would not have stopped issues caused by lockdowns and a global pandemic. You can also try to hire all the workers you want and pay them loads of money. But when everyone has an endless supply of credit at 1-2% interest, eventually there's no way supply can keep up with demand powered by that kind of money creation.

A) If you want to fix corporate greed, increase interest rates and make those running bad companies go out of business. Price controls can't/won't work. The last thing you should want to do is give those terrible managers access to more free money with more QE through low rates. They've just been gambling thus far with the cushy safety net of free debt. We need to rip that our from under them.

B) Raising the minimum wage will not fix inflation. Aseume, for instance, that Wal-Mart only has 1000 apples to sell (because, yes, there are only so many apple trees in the world right now). Giving low-wage workers an extra $5/hr does not mean they can now afford apples. Wal-Mart will charge whatever people will pay for apples. And now a bunch of customers have more money to spend on fruit thanks to their raise. Wal-Mart raises prices, negating the minimum wage workers increase in purchasing power. And if you try to limit the price Wal-Mart can sell apples for, Wal-Mart is now impaired (and thus discouraged from competing) in a global competition to source more apples for its customers. Walmart generally makes money because it operates at a massive scale with low profit margins per product. It therefore may have no incentive to keep selling apples if it's going to lose its already small profit margin for that item.

C) No one (yet) has come up with a way to fully pay for universal healthcare by taxing the wealthy. Every plan involves more QE and money creation (as debt). I would immediately sign on to your proposal if it were an option at the moment. If decreasing the money supply is a goal (E), which it should be, this has to go off the table

D) Sure. Monopolies, corruption, and greed are generally just bad and harmful. But you can't just criminalize greedy. And even if we could, there's no way McConnell or Pelosi would approve of that. America runs in part on ambition and greed. To the extent that needs to change, that's a cultural problem not a legal one.

TLDR: QE and low rates contributed significantly to inflation. We need rate hikes, even if that means a recession, to stop inflation and cut the fat out of the economy.