Even if we levelled all wealth, life would be limited by the finiteness of resources, and only economic development - which this levelling would inhibit - would alleviate such scarcity.
Consider what would have happened if society had followed John Stuart Mills' advice in 1848 and maximized for equal distribution of income, resulting in per capita GDP barely increasing from its $2,000 level over the last 170 years:
"It is only in the backward countries of the world that increased production is still an important object: in those most advanced, what is economically needed is a better distribution"
-John Stuart Mill, Principles of Political Economy (1848, book IV, chap. VI)
One possibility is that such an egalitarian society would have produced more brilliant engineers and economists, by providing more opportunity to manifest one's talent to lower economic classes. And they then could, perhaps, figure out the unsustainability of their trajectory earlier, and correct it to produce somewhat slower but steady growth without environmental catastrophes, translating to better long-term outcome.
A per capita GDP of $3,000 wouldn't have provided people with the surplus time to dabble in engineering and economics. It's a living standard that today we categorize as extreme poverty.
Eliminating involuntary unemployment doesn’t require levelling of all wealth, it just sets the floor price for labour and maintains a buffer stock of employed people ready to be hired rather than a buffer stock of unemployed people who are less ready to be hired.
Without forcing people to work, it is impossible to eliminate involuntary unemployment. The government using tax dollars to offer people jobs that don't match what they're seeking would result in them refusing to take those jobs, and remaining involuntarily unemployed.
