You should not expect a better payment from your company because you are a better programmer. Payment is according to demand and offer. Your company will mostly demand what you say: OK engineering, management skills, good communication skills, getting well along with your colleagues.

But from being a better programmer you can still derive better monetary gains. Instead of striving to become a lead or manager or product owner, you can either become an entrepreneur or search for a company where being a better programmer is a highly desired skill.