inheritance of wealth does not go well with your people are born equal. you can only have one of the options.
That is a gross distortion.
Born equal has nothing to do with family, gender, health, wealth or anything other than civil rights. In other words, there is no nobility or other political privilege or punishment by right of birth.
If anything, being born poor is now currently breaking the "born equal" promise because the state provides more for those at the expense of those whose families pay their own way.