>What "plunge" are you talking about? Even the famous (but flawed) graph from epi shows a very small dip:
https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcSDmFnp.... Also that was in the 80s, not the 70s as you claimed.
https://www.epi.org/publication/americas-slow-motion-wage-cr...
Again, growth is overstated because CPI is flawed and tends to understate the actual growth of cost burdens. So the "slow growth" mentioned here is people losing ground.
> If it dips a little then returns to previous levels
That's the problem: it didn't. Your assertion that it did is based on an unnecessarily limited data window. Zoom out, and you'll see a declining standard of living and a lowered ability for Americans to take their wages and buy durable goods (colloquial denotation). The declining birth and home-ownership rates for younger generations compared to older ones at the same age did not just come out of nowhere, and the general increase in debt load is part of the answer to why the entire thing hasn't collapsed yet.
>Which specific components do you have issue with? Moreover, the cpi is supposed to represent the country as a whole
The link went over many, and I would hope that you'd have read it and not asked that question. But, as a general gripe: its basic nature as an index makes it game-able, and the people who make the decisions about what goes into it have a conflict of interest: they answer to the people who answer to voters (more likely to be older, monied, white), and the people who can pay for votes. You might say that it's a coincidence that it then tends to show less of a crisis in income and purchasing power than many (younger, poorer, not white) feel exists, but I'm not so naive.