I can’t comment on the nostalgia aspect, because I wasn’t alive back then, but I can say that there are several aspects of the statistic you used that make it not reflective of the experience people have.
One issue is median real income does not tell you anything about the distribution of income. It can be used to show that the top 50% of people have had “real income growth”, but can hide a lot at both extremes; the poor and rich have had vastly different experiences [1]. The metric on that page looks at “share of national income”, so it has issues as well (not anchored to any objective measures), but it illustrates my point just as well.
The bigger issue I find is the way that “real income” is measured. There are a slew of issues, IMO (hedonic adjustment, for instance), but the biggest is the way that asset prices are treated in CPI - that is to say, they are not! Shelter prices reflect “owner equivalent rent”, not the price to actually buy a home, which has ballooned massively in the last few decades, especially the past five years, relative to income [2]. The same applies to other assets such as stocks; they are nowhere in the CPI metric, but have a direct impact on our lives; higher-priced stocks impeded the purchasing ability of people with respect to stocks, costing them returns over time (couple this with the larger cost of other assets over time and it is clear retirement age will have to go up). So, yes, maybe real income has increased, but substitutions are being made and tricks are being played; more people are renting longer because of home prices. Future returns on investments will be lower because of a giant asset bubble.
Also, future liabilities are nowhere to be seen in the real income metrics. The national debt that the US has saddled its current and future citizens with is shameful and will inevitably cause financial drag in the future (could be higher tax rates, but my personal bet is persistently higher inflation over time; you can already see the Fed giving up on its 2% target).
[1]: https://wid.world/country/usa/
[2]: https://www.visualcapitalist.com/median-house-prices-vs-inco...