After playing these games, asking other players/admins, and reading online I am led to believe that Quake Live and Battlefield 3 are frequented by bots and there are plenty of hacks of various kinds. I'm confused how this is possible, or even easy seeing how many players have access to these kinds of "tools" (sic).

Isn't it possible for the game authors to digitally sign the game executables so that when they run, the server can ensure only the allowed client is sending commands, thus preventing any kind of abuse? I.e. every player command would be signed by a private key, or symmetrically encrypted (not sure which would make more sense).

I understand that players can look at the running executable's behavior (memory etc.), but if games are apparently so easy to hack, shouldn't most apps be hacked as well (e.g. Skype, all DRM running on Windows etc.)?