Not sure I like the term "over-utilization" it's more likely over-consumption and under-utilización.
The industrial revolution was arguably a by-product of huge amounts of wealth in the hands of a few.
Efficiencies of scale may exist, but are not dependant on equal or inequal distribution of benefit.
Seems to me historically rich people/nations have consumed more natural resources, often taking them from other people/nations, focusing not on global wealth creation but on moving resources in, at the expense of global wealth.
On a global scale, inequality seems to have led to more consumption and destruction of someone else's long term resources.
Equality seems to lead to more resource preservation, thus better utilización.
Inequality is the result of thinking about yourself at the expense of others, equality is the result of thinking about others, and those targeting equality are likely to include future generations in their definition of "others" and thus more efficient/conservation use of long term resources.
Interested to see any stats to back up the assertion that "reducing inequalities typically means more consumption" on a global scale.