Does society have an ethical responsibility to assist the next generation in succeeding?
There are a lot of meaningful words in the question. What are the ethical responsibilities of a society? Ethics are agreements. Law formalizes those agreements, and society is bound by its body of laws. The next generation has the responsibility to add, modify, and delete the societal body of laws, when they become capable and able enough to do so. Ethical responsibility has a very limited scope. There are other things involved in societal behavior. Given the five divisions of social systems it is more important to monitor historically the direction and intent of the society.
You could ask, is it the intent of the laws to moderate the systems that exist - to produce the outcomes we observe in society or the world today? We can view law/ethics as producing the status quo. President Trump is a product of United States society, his family, the guidance given him through life, and his own free will. Can you blame him without asking if the society is intentionally directed toward producing his output?
The rich get richer, and the poor get poorer. Can society moderate that? Yes, through first aligning intent and direction, putting focus on goals that will attain the agenda, and codifying the rules used to successfully accomplish the tasks in the agenda. Traditionally, parents have had the obligation and rightful authority to at least provide formative guidance that will tend their children towards gaining the knowledge and power needed to successfully negotiate successful movement within society. After that, society expects citizens to participate in task accomplishment according to it's rules at minimum. Adults are allowed and even required to add, modify, and delete aspects of the society itself to align or refine the society's goals and directions. Society is not created for us. It is created by us.
What I have observed is that the more educated a person the more difficult problems the person will be asked to solve. Third graders solve third grade problems. High-school graduates are trusted to solve high school level problems. Doctors solve problems at their level of engagement, and the third grade problems. So, effectively, the more you know the harder you work. People have an ambient way of forcing that on each other it seems. It never gets easier, so we strengthen ourselves to meet the challenges.