Not really, no.

I suspect the people in charge are older than I am, and their "memory" of Russia being the enemy during the cold war defined how they permanently think about Russia.

Once you setup an organisation, even if its purpose ceases to exist, that organisation takes on a life of its own. NATO is one such organisation. Nobody chooses to terminate their own job. So NATO just grew and dreamed about controlling everything, making the whole world peaceful eventually.... but except not Russia, Russia wasn't allowed (they are tricksters! can't trust 'em! or so some people think).