I am not going to change the way I play the game because of this STUPID flawed and overpowered system.
Nor should the rest of us be forced to play your idea of what the game should be.
There's an issue with that strategy anyway. The AI will take advantage of your weak military and declare war, or bug you asking for tributes all the time. Of course you'll probably say you have to keep your military rating "near middle of the pack". No--still lame and too restricting, and I don't feel like keeping that close a watch on it JUST so I avoid agent spam. OMG the system effects the entire way you play the game and you see nothing wrong with it, and nothing wrong with the fact it can't be turned off?
That is indeed an issue. I won't pretend it isn't, but it beats the alternative - being spy spammed and gang jumped by multiple simultaneous declarations of war. If anything, I tend to keep my military too low - I occasionally have minor civs ranked higher than me because I spend more time building my economy than my fleet. Guess what? It's survivable, as spy spam is apparently not.
No matter what you do to the espionage system, it will efect the entire way I play - to think otherwise is idiotic. HOW it affects gameplay might be discussed, but that it will affect it is not questionable. Even turning it off would cause massive changes.
Agent system needs:
1) Passive espionage
As previously stated, you will be seeing this again in 2.0, unfortunately. Undefendable passive spying is a lame cop out.
2) A reasonable and REALISTIC way of calculating agent training costs
Would you please define what that might be for me? Remember, it must apply to everyone equally, so if you get hordes of dirt-cheap spies, so will all of the AIs. Otherwise it's just a hardcoded player advantage. Even if they took the silly "based on how many active spies you have" stance, your spies would STILL be outnumbered several times, because removing the AIs spies resets their costs as well.
3) A TOGGLE to turn it off entirely, because it is boring.
That would be a defendable option, as long as it turned off all espionage, period. I might even try a few games that way. It's unlikely to ever be implemented, though.
I think most of the problems you are facing with spy spam is that you are playing the exact wrong level. At lower levels the AI can't afford to make spies, and is too stupid to use them anyway. At higher levels, the AIs have more resources, making it much harder for you to get yourself into this situation in the first place. I've never tested it empirically, but that seems to be the case.