Another area which got me thinking is dynamic encryption where the game is reencrypted - or at least most important parts - between play sessions. I even read a couple years ago about dynamic encryption which ciphers parts of the game while being played so that the state is never the same from moment to moment. Decoy false memory and dynamically encrypted memory will probably become practical in a few years, too, which will make it much harder to pirate.
I believe that technology advances will eventually make games secure from all but the insider security breaches.
Personally, I doubt it. As computers get more powerful, breaking security becomes even quicker and easier too.
Even if your suggestion worked, you're once again saddling your users with potentially severe issues and DRM shouldn't step on the toes of the people supporting your product. Changed computers? Your saves are probably not transferable, unless key encryption information is stored along with it, potentially giving crackers the information they need. Abrupt termination? Your game might be scuttled completely, and your save data irrevocably lost. You might even lose the game you paid for if you've used up all your installs, and a ruined copy can no longer phone it's deactivation home. Plus there's always the possibility they can simply spoof or bypass the encryption altogether.
You already hit the nail on the head, anyways: Quite a few breaches are zero-day, from first run pressings and internal leaks. A few cracking groups offer compensation for anyone that can get a pre-release to them and there's many opportunities along the chain for an underpaid, uncaring, or disgruntled employee to slip a copy into the wild.
As wiser folks than me have pointed out, that effort should be spent on delivering quality content consumers are willing to pay for, not erecting a feeble barrier to slow down people who wouldn't give you a bottle of water if you were on fire.