I think you will be okay if the cookware is of decent quality and the SS layer is adequately thick. I have been using Revere Ware, and occasionally an old iron skillet or Dutch oven for most of my life. Revere ware has a copper bottom.
I did use visions for a while and corning ware.
Both the aluminum and copper are used to help distribute heat evenly as they are good heat conductors… but I agree that you do not want anything you eat to be cooked in an aluminum pot.
One thing that helps is to never cook your food on more than a medium heat, the hotter the heat the greater the potential for leaching from any metal.