Re: The only case where you cooperate with the designated enemy
The Soviet Union was the designated enemy, but Russia (the descendant of the SU for you kids) has been pretty much ignored by the propaganda machine until recently. The oligarchs, after wasting Libya and Iraq, wanted to subjugate Syria & Ukraine, but Russia objected. Russia, thus, was again designated, and its enemy status was pushed further when the Democratic party thought it would be advantageous.
Modern kids don't see Russia as an enemy; only old farts indoctrinated during the better-dead-than-red era do.
Wasn't Russia our biggest ally in WWII? (Never mind the War of Independence.) Didn't Russia provide us with information about Afghanistan after 9-11? Didn't the Russian Federal Security Service (FSB) warn us (twice!) about the Tsarnaev family (Boston Marathon bomb)? Doesn't Russia ferry our astronauts to and from the International Space Station for cheaper than it cost us to do it with the Shuttle? Doesn't Russia provide NASA with RD-180 engines to power rockets?
In short, a cooperative cyber security operation is certainly doable. It's a very good idea too. It's just that the ColdWar2 politicians like opposing it.