What makes you think people would become better than they are right now?
Rich people who inherit so much they never have to work or worry about bills can be unhappy, lonely, unfulfilled, or just plain unpleasant right now. (Yes, I know, not all of them).
People without jobs or money worries can be criminals, can steal or commit violent crimes, can lie & harass.
Not all crime is motivated by money.
Rape is about power, so are many other crimes, so crime wouldn't be virtually eliminated - why else would multimillionaires be caught cheating on taxes or embezzling funds?
Not trying to say all wealthy people are dreadful, but just like everyone else, not all of them are perfect happy human beings living fulfilled lives.
Some people will still have more than others, some people will be envious, some will fall through the cracks & have terrible lives, some children will still need social workers, some people will still be murderers.
Some people will still be wildly talented at something (e.g. singing, mathematics or writing) while others are not & they will still feel envy.
Some people will still have lots of get up & go so they'll do something with their lives, while others won't bother to get out of bed except to use the bathroom.
People won't all be on an equal footing because people are not all equal in drive or ability no matter how equal their chances in life.
Why do you think will human nature be different just because someone else will be doing the 'jobs'?