You have to be very wary of the fact that the Gini coefficient is a unique characteristic of a distribution, not of an economy. You could calculate a Gini coefficient of the number of hairs on people’s heads. Very commonly people confuse the Gini coefficient of the distribution of income with the Gini coefficient of the distribution of wealth.
Gini coefficients of income get into differences between the distribution of income before the effect of taxes and transfers and after taxes and transfers, also, the difference between the distribution over individuals and the distribution over households. Then there is the effect of transfers-in-kind such as public education and free health care, and public services such as effective policing that obviate expenses rather than increasing what is recognised as income.
As for Gini coefficients of wealth, they are fraught with problems with valuations and exclusions. Home mortgages are customarily included but home values are not (which stupidly counts middle-class people with millions in home equity as being poorer than the destitute homeless. Student debt is counted in countries that have it, but the value of professional skills and oligopoly licences is not.
And then, of course, there is the issue of wealth and income that don’t officially below to any one person, but which may have very different effects on real material inequality, depending on what benefits they produce for whom.
The idea of making up a scale with limited discrimination and qualitative definitions is probably compelling. I must get around to it some day. Perhaps using star and half-star emoji.