We don't see shopping cart inflation because it's countered by the technological cheapening of the production. And the key fact that new money is not being given to people buying groceries.
It is easy to forget that the Fed's mission is to stabilize the value of money, not to conform to some concept of fairness. I would also point out that instability in the value of money disproportionately impacts the poor, who have the least savings available to deal with price shocks (if you are living paycheck to paycheck, then the price of bread suddenly doubling will leave you eating half as much bread).
The Fed's activity is what drives the government's ability to pay it's contractors.
If you want to increase the money supply, print some money and give it out.
If you want to fund highway construction, figure out how much it will cost and then raise that amount of tax revenue to pay the builders.
Without sarcasm, given the latest purchases of assets beyond Treasuries and MBS, why do you think the Federal Reserve has purchased assets at market rates?
Congress decides how the money is distributed when they're spending it.