It's not likely that it will happen however I think sole cookie based tracking should go away anyway. There are other ways to do it as well. Part of the reason many programs don't use them is because they don't want to. They make more without them.
Even if it did happen it's still not necessarily the end of the affiliate system as we know it. There are ways around it. Both technical and not so technical including using a multiplying factor to determine payouts. For example, if it's determined that 40% of users have it on then you would multiply the affiliate payout accordingly to compensate for the loss to the affiliate due to tracking problems. Now whether sponsors would actually have the decency to do this... another story (some loss already occurs but we don't see many sponsors offering an extra 10% etc over it, do we?). And there's better solutions of a more technical nature to help with the problem anyway.
Some other ideas off the top of my head:
1. white labels / specialized domains for an individual affiliate
2. Referrer based tracking (to compliment existing systems .. few block referrer data)
3. IP based tracking ( to compliment ...)
...