There are people who would tangibly benefit from a new cold war everywhere, possibly except Ukraine. Imagine how much of a useful distraction it is all around. The only people losing are regular citizens who just want to live and prosper.
But we need to thread carefully here. The other side looks that it might involve non-rational actors. Hopefully they're also incompetent and not very united amongst themselves.
I'm pretty confident that when Russia would be a real democracy, it would have grown closer to EU. I know some Russians (the same as I know some Ukrainians), and I'm sure they would prefer our countries doing more collaboration.
But now we are all stuck with this KGB-er that still thinks he's living in Soviet days.
It's become very clear by now that the west shouldn't do business with non-democratic countries. We made the mistake with Russia and with China, and our money only makes them stronger. It doesn't push them towards democracy at all.
If you use e.g. the democracy index, you leave most of Africa (which, remember, is bigger than it may look on a typical map projection) and Middle East, which fare as bad or worse than Russia, to China. Try suggesting that to US corporations or foreign policy lawmakers.
Once more than half of the world gathers behind China due to sanctions, give it time to snowball and soon EU/US/AU may just become unable to compete with Chinese offers, meaning any remaining country will have no economic reason to continue dealing with the Western bloc (except if you threaten them, bribe top officials personally, or do a coup).
Edited to clarify implications.
But I think we've been a bit too free with sending our money to those kind of states.
The people of Russia and the EU would 100% love this if you were to take away all the propaganda. But this view doesn't seem to be shared by the ruling elites and the US doesn't seem want to want to allow that profits made from "Marshall money" fuel in any way the development of Russia.
And there's also some mindset incompatibility that would need to be resolved first:
Western European countries have actually accelerated their development through fierce competition and even war amongst them... I think this is what in the end lead to the enlightenment and then the industrial revolution. But war was kept in check in a way, it was "war by the rules" sort of with conditions to limit destruction of intellectual and material capital. People died, a lot, but knowledge, tradition and core assets too, were preserved. And "being able to play The Game right" is still a fundamental condition for "joining The West(ern Europe)".
Russia doesn't seem to get how to "be corrupt, but not THAT corrupt" (eg. there's corruption in France and Germany too, but it does NOT undermine the foundations of society - there are soft subtle limits that people learn how to thread around). (+HINT: you can't remove corruption and nepotism 100% without, paradoxically, getting back to 100% corruption and nepotism because you'd need to centralize authoritarian power to fully/absolutely solve corruption. "All or nothing" thinking doesn't work. It's always "pink" or "gray", never red&white or black&white. It's subtleties and mental gymnastics like this that make Western Europe what it is and give its power, this "the hidden soul of Europe" in a way, "discretely weaponizing subtlety and paradox for the purpose of furthering the development of humanity, science and knowledge". And it's stuff you'll not find in any book. It's stuff that people need to figure out by themselves and also let other figure it out by themselves.) Or that "you can only get into a real hot war AFTER you've won at least say ~50% of the `war for peoples' harts`, so that in the event of a victory you can maintain power without having to `break people into submission` by physical or mental violence". Or that there's an unwritten rule between "proportionality of assets and power - you can't hold immense political or military power in your hands if you're not backed by the people holding most assets, and you can't hold assets without having them taken or severely taxed-away if you don't also assume political responsibility and power, even indirectly". And so on and so on and so on...
Russia just doesn't seem to grok the underlying unwritten rules of western civilization...
Neither does eg. China, but they're not expected to either. Russia keeps wanting to "come and play" with Europe, but they just can't get rules of the game / the dance steps. And sure, the rules are in slow but continuous evolution, but that's the thing, figuring them out and then figuring out how to keep figuring them out and keep playing "the good game".
To conclude: you'd need to solve both (1) US opposition and (2) mindset incompatibility, and I think this is REALLY hard (not impossible though), in order to get Russia and Europe together in any meaningful way!
But like you say, these things need to evolve, and with older generations dying, a part of their mindset dies along with that. You see young people getting more into the mindset of the west.
I think this is more like incompatibility between the "central-continental European cultural area" (+ some "balkanic-European c.e." elements for Hungary) and "west-atlantic-postcolonialist-European c.e." and this is very mild and will go away when current politicians trade seats. Hungarian, Polish, Bulgarian, Romanian etc. people can cooperate well amongst themselves and with eg. Germans or Austrians, if nobody is deliberately stirring hate.
Maybe Poland and Hungary could serve as bridge to Russia to solve the worst incompatibility, that between the mindsets of west-atlantic-postcolonialist-europeans and mindsets of russian-europeans. But I would not have much hopes, these two groups are very incompatible... each would probably find it easier to get along with the Chinese or the Americans that with the other. And there's also eastern European countries like eg. Romania that have better closeness / similarity / affinity to west-atlantic-Europe and the US than to the central-European ones and would rather burn themselves than serve as a bridge to Russia... Europe is complicated...
German (continental) European de-facto-leadership + eastern Europe to be the bridge could work in theory though...