You have this backwards. Inflation (via CPI) is based on price changes, it doesn't cause them.
>would be much more believable if the businesses selling the "inflation impacted goods" we're making the highest profits ever, far in excess of the highest estimates of inflation.
This is exactly what you'd expect when there is low supply and high demand.
If, for argument's sake, a dollar halved in value, the price of a widget of constant value would double to maintain equality in the exchange. What makes things complicated is that the value of the widget isn't constant and can also change over time, so we can't just look at that widget to see how the value of the currency is changing. Instead, we try to look for price trends across a wide range of products (CPI) to try and infer what is related to currency devaluation rather than changing values of other goods and services.
Housing is the biggest component in CPI: something like 40% IIRC
[0] https://www.bls.gov/cpi/factsheets/owners-equivalent-rent-an...
Some back of the envelope estimates:
The last mile is usually going to be the largest expenditure of fuel per dollar of product transported. A semi truck gets 5 mpg on the low end and with diesel fuel currently at $5/gallon, that means it would cost just $2,700 in fuel to ship an entire truck load from New York to Los Angeles (much farther than most products would ever be trucked). Assume the truck is loaded with a low price, low margin product like toilet paper and you might ship around 4,000 small packs of toilet paper for a total fuel cost of $0.67 per roll. So if fuel prices doubled to $10 gallon, you would be looking at an increased cost of $0.67 per pack of toilet paper that is normally, maybe $10. So you are looking at a 7-10% increase in the cost of that toilet paper due to a doubling of fuel prices.
Of course, fuel is needed for the equipment that cuts the trees and the energy to manufacture that toilet paper, the plastic it is wrapped in, etc. But, we have to remember that we are talking about an inexpensive yet bulky product that we are shipping across the entire US and the weight is low so you could probably drag two trailers of it with only a marginal decrease in fuel efficiency.
The reality is that most products are trucked much shorter distances from ports that use enormous container ships where the fuel cost per dollar shipped is vanishingly small.
I've experienced the opposite several times because I don't consume a few things that are part of the basket.
Your claim also doesn't explain how inflation didn't balloon in countries that provided actual financial support to people - the US had two payments of next to nothing, most other countries provided continuous support, even those with far less per-capita income.