The (almost) last US ambassador to the former Soviet Union was Jack Matlock. He held the post between 1987-91 when he was based in Moscow. He had been based there earlier in his career in the early 1960s and was there during the Cuban missile crisis. He testified in front of the Senate Foreign Relation Committee twenty five years ago, saying:
I consider the administration's recommendation to take new members into NATO as misguided. If it should be approved by the US Senate, it may well go down in history as the most profound strategic blunder made since the end of the Cold War. Far from improving the security of the US, it's Allies, and the nations that wish to enter the alliance, it could well encourage a chain of events that could produce the most serious security threat to this nation since the Soviet Union collapsed.
Matlock testified against building up NATO because he felt NATO had succeeded in its aims, that was to forge a Europe that was "whole and free" and to go further would again precipitate an arms race with Russia. Moreover, Russia after the collapse of the Soviet Union wasn't endangering the security of any East European nation as it had accepted their democratisation under Gorbachev. He also felt that:
If it was a process we started then, if continued, and if continued up to the borders of the Soviet Union - I mean the borders of Russia and included former parts of the Soviet Union ... such as, most importantly, Georgia and Ukraine, that this would bring about a confrontation.
Instead, he considered that the real task ahead was to build a new security architecture for Europe that would include Eastern Europe and Russia as well as other states that had been in the Soviet Union. At that time, there were concrete proposals that had been planned out - the Partnership for Peace and they had an organisation, the Organisation for Security and Peace in Europe. Obviously, this was not the route that was finally taken.
As for your own remark:
NATO practically exists as a counter-point to Russia ...
This betrays Cold War thinking and let us recall the Soviet Union was dissolved thirty years ago and further recall that in 1997 NATO & the Russian Federation signed the Founding Act in Paris of which the preamble states:
NATO and its member states, on the one hand, and the Russian Federation ... based on an enduring political commitment undertaken at the highest political level, will build together a lasting and inclusive peace in the Euro-Atlantic area on the principles of democracy and cooperative security.
NATO and Russia do not consider each other as adversaries. They share the goal of overcoming the vestiges of earlier confrontation and competition and of strengthening mutual trust and cooperation. The present Act reaffirms the determination of NATO and Russia to give concrete substance to their shared commitment to build a stable, peaceful and undivided Europe whole and free to the benefit of all it's peoples.
Making this commitment at the highest political level marks the beginning of a fundamentally new relationship between NATO and Russia. They intend to develop, on the basis of common interest, reciprocity and transparency a strong, stable and enduring partnership.
Russia signed a partnership deal with NATO but had ambassador Matlock suggestion been followed up and pressed on with, there would have been a single new security architecture for peace, prosperity and security that would have included them both and that would have been a far better path to follow as it would have left the "vestiges" of the Cold War where it belonged - in the dustbin of history, rather than, as we are now, being in danger of reviving it.
Sources: NATO & Democracy Now