Disclaimer, not an economist but work with a bunch of them. Of course, economists are already hyper-aware of focusing on a single measure and of all these issues with specific indicators, and surprise surprise, we have a wealth of alternatives that are published and are freely accessible all the time:

e.g. the BLS already releases all manner of alternative unemployment statistics (see "discouraged workers"): https://www.bls.gov/news.release/empsit.t15.htm

e.g. for income inequality, a crude but well known measure is the Gini index which measures how dispersed incomes are in a population: https://fred.stlouisfed.org/series/SIPOVGINIUSA#0

e.g. Consumer price index is another approach measuring access to basic goods: https://www.bls.gov/charts/consumer-price-index/consumer-pri...

Household net worth is another one that the article mentions.

The matter of which number is chosen as the official measure of "goodness" is the real issue and that is a political matter, and because depth of public (and shockingly often policymaker!) discourse on the matter is stuck at "did the thing go up or down". I'm dubious that switching to a different indicator will solve the problem per se - perhaps make it harder to game.