When people talk about a 'fairer society' I always ask for an example of a fair society and no-one has ever been able to give me an example. As has been said the greatest obstacle to a 'fairer society' is human nature. My mother lived on her state pension, she got help with her council house rent but she didn't find it hard, she had always lived within her means even when we were children and dad was working. Her neighbour told her that we were lucky to have good jobs and nice homes. Her response was Yes, the harder they've worked the luckier they've been!
When I was still teaching we all knew roughly what each earned, publicly available pay scales but how people used that money differed widely, some spent the month building up an over-draft, paid it off then started again. Nature being what it is I, and those like me, who lived within out means were the ones mocked and sneered at, how could we afford regular holidays, school fees etc..
As for lessons in schools on money management, thought I'd strayed into the Dm site, schools responsible for everything.