> No, there are not.

Yes, there are. What a tiresome exchange.

What the CPI represents is rather narrow, which is described right in the CPI reports, along with links to their numbers
https://www.bls.gov/news.release/cpi.nr0.htm

Ultimately the faith in the CPI depends on what you want to ignore. The sampling is 29% of the wage earners from the most populated centers.
https://www.investopedia.com/articles/07/consumerpriceindex....
Of course it's biased toward consumerism, but that's a huge problem with calculating the cost of anything today.
Even with that caveat, is that a 1.8% increase in shelter cost from 2019-2020? That's not realistic.

Like the unemployment rate, these stats have long ago become politicized to the point they are a reflection of what needs to be portrayed.
These numbers (CPI, GDP, Unemployment, etc) can and are manually changed by whatever ad-hoc method that is convenient.
It's important to have some insight as to what's going on that would result in a huge disconnect, rather than handwave off the "cranks" who must be complete morons because they are "the other side".

> So if the GDP grew "only" ~2.5%, then any inflation above that, would mean were actually in a recession/depression for the last decade

What you consider a recession and I consider a recession are different things. Consumerism skyrocketed and domestic manufacturing cratered.
Commercial property has also bottomed out. The velocity of money has slowed ~2012 until we're at the height of efficiency in velocity...which is molasses.
Money doesn't move on anything that isn't land, because that's the lowest risk at this time and middle markets/individuals are failing or barely subsiding.

> If inflation is >5% (per the truthers), then the economic growth would have had to been on top of that, for a nominal growth rate of >7%.

Economic growth is about debt growth, like it or not. All the new debt is in real estate (stocks and bonds for companies and individuals), which is where the inflation is living.
see property prices in Los Angeles growing at about 7% year over year, same as a bag of cheetos and wholesale soda costs...but the monopolies are still duking out loss leading with $1 fountain sodas so nobody cares.

Property is immune to the deflation (cannot be outsourced, et al) and the only debt that banks are interested in, on a risk basis.
Due to the ungodly improvements in efficiency (and outsourcing) most goods have been subject to massive deflation and have made the functional monopolies
(and new tech) look super valuable, driving the tech stock frenzy. Unfortunately, those efficiencies have been maxxed out, more or less.
You won't be seeing TVs drop from 700 to 70 (like they did from 7k to 700), the will go back up along with the food prices that have been slowly rising.
This rise has been balanced out by the fantastically low prices of goods (eg 40oz Bag of Cheetos have risen just under 10% year over year) or loss leaders duking it out ($1 sodas from Hardees/McDs).
Too bad your fast food is still routinely over 15$ a person.

I don't think it's prudent to throw my hands up and say "I just don't understand why things are the way they are, when I have a single number to tell me everything is ok."
The CPI is a garbage index. There are reasons why the markets are the way they are and it's not hard to see, regardless of what the US gov wants to say about it.