>Paying more/longer requires more money. Where does that money come from?
Cut the number of postdoc positions in half, double the salaries of the remaining positions, and make it much more competitive to get a postdoc. The purpose of a postdoc is a final training step for someone to become faculty. Only people who are clearly faculty material after finishing their PhD should even attempt a postdoc. Unfortunately, many professors take on postdocs who have no shot of becoming faculty because their lab runs on the cheap, experienced labor they bring.
Remember, the replacement rate for academia is exactly 1 postdoc with faculty aspirations per lifetime of each professor. Anything >1 and academia must grow exponentially to accommodate every single postdoc who desires a faculty position. Most professors have >>1 postdoc over the course of their careers, which means there are way too many postdoc positions in the world.