Would that be pragmatic to implement on a large C++ application that runs on millions of machines? The application is at the mercy of the OS when it comes to memory access. A user has full access to the whole machine, so they can always starts processes with privileges set to allow them to read from other processes' memory space.
This is assuming a 'regular' environment - today's hardware, with a multipurpose OS that allows several simultaneous programs to run, etc.
If you try to look at this a a cryptographic problem with a private and public keys, currently there is no way to hide a private key you use in your application from the hacker.
Once the hacker finds your private key, he can use it to emulate your application - and all you can do is to make this somewhat harder.
Some partial solutions are possible in multiplayer games, where part of the game is run on servers.
This technology, of course, doesn't protect from physically reading the memory from the memory chips by the hardware tools, but protects from a spying process perfectly well. Apart from that, running inside a VM and modifying memory from there is another strategy, as was brought up below.
My point was that any mitigation strategy will be broken by a determined attacker - it is inherent in the open structure of the PC hardware and OS. Blizzard faces are very determined, there's money to be made with auto-harvested gold.
If you want to achieve a real security, not only obscurity, this needs to be done at operating system level.
This is a part of what is called Trusted Computing, something which was talked about a lot in the past years but no real progress was made (you can search for Microsoft Palladium for one example).
I play the online game World of Warcraft, which is plagued by automated bots that inspect the game's allocated memory in order to read game/player/world state information, which is used to mechanically play the game.
They also sometimes write directly to the game's memory itself but the more sophisticated ones don't, as far as I know.