"The Internet" is not the entity seeking advertising revenue from the websites you visit. Those would be Companies X, Y and Z, and Individuals A, B and C... This is like saying you've contributed to mankind by being a teacher and helping Johnny with his arithmetic, or hell, even as a surgeon training other surgeons to save lives - and that this should mean you can rock up to McDonalds and claim your free happy meals.
A number of sites do have exactly what you're talking about - an option to throw them a couple of $$ (either as a lifetime payment or a subscription) in exchange for an ad-free experience. Personally I just use the free automated ad-blocking technology available, since it's simply best practice when it comes to security, to block as much third-party content as possible.
We do already have a 'points' system, by the way - it's called 'money'. If you wish to be rewarded for what you do, you find a way to either get paid by someone else to do it on a regular basis (employed or contracted), figure out a way to make a business out of it yourself (self-employed), or provide it as a purchasable product (sales). If you're simply doing it for the warm fuzzies, well - you should have those already