You should care about equality because inequality tends to make places worse for everybody. Yes that includes those rich people. You can't go to the beach because it's all built full with private resorts. Those rich people can't walk the street and have to live in walled villa's for fear of crime. They also can't easily get married to who they want because they have to hold their assets. Vietnam is poorer than South Africa per capita, but significantly safer and more pleasurable to live. Would you rather be top 10% in South Africa or Vietnam?

What is interesting is that this was true centuries ago too. Life as a noble in the middle ages was stressful as hell and you couldn't even decide on your own lovelife. Read Seneca and the first thing he writes is that Augustus (whom he knew personally) was constantly complaining about his busy life and dreaming of a retirement that never arrived.

Rank order of income inequality (and coincidentally wealth inequality): South Africa > US > Vietnam

Rank order of preference to be top 10% in for me: US > Vietnam > South Africa

So your method does not disabuse me of my belief. It’s quite clear that equality has not made Vietnam more desirable than the US. In fact, there are some 400k foreign born in Vietnam (<1%) vs the US having 15% foreign born (a stark enough difference made worse by forcing foreign-born to be from non-neighbors). So I must reasonably conclude that my rank order is likely shared by others and that others too are not, in fact, lured by equality.

There is an old immortal tweet: cars have windows and go; houses have windows and don’t go; so it’s not the windows that make things go.

If inequality were as critical we’d expect a perfect rank ordering of distant migrant population attempts matching it. The numbers are so vastly different that one cannot conclude equality is of great importance to most.

Inequality by itself doesn't cause bad safety. the following countries have a higher share of wealth controlled by the top 10% than vietnam and also a lower homicide rate: singapore, uae, switzerland, sweden, qatar. that's just off a very quick search i'm sure there are more. Certainly in none of those countries are people hunkering down in private fortified castles for fear of stepping out in public.