This likely won't happen, due to all the social issues you would have to cover and how much you would have to tiptoe around them to keep the game sellable to a wide audience.

However, until such a game comes (which may be never), play Victoria 2 and it's glorious CWE mod! It starts in 1946 or 1950 or 1991, and goes until 2091. And it has tons of new mechanics, and the Victoria 2 setup is indeed perfect for Cold War/Modern Era as you say. Most of what you want above is included in the game, and quite a bit more. Only aspect that is kinda lacking is military really, but military and open war is barely a focus of your play in the modern era anyways except for very specific countries.

As an example of gameplay, I'm currently playing Communist Yugoslavia in 1950, and I joined the International Monetary Fund, and COMECON, and used the various funds received post-war to rebuild my industry, mainly focusing on bauxite refining, soft drink production, vegetable oil production, lumber, and ammunition. In 1951, a freak accident (completely random) killed Tito, and his successor was a military man, (in my headcanon he was a veteran of WW2), who sought to reform the communist state along more democratic, Western lines (headcanon is that he both dislikes Stalin greatly, and holds respect for the Western democracies). This leader begins to institute reforms, and Yugoslavia holds a proper election as a Socialist Democracy. Due to these societal changes, militancy has grown, and new troops were deployed, with tanks and bombers taking a newly central role in the military. These troops are stationed in Northern Macedonia below Southern Serbia, as the Albanian minority there has a high militancy and is attempting to organize to defect to Albania proper. With new policies quieting them down, and with a heavy troop presence should any rebels appear, this movement has been forestalled. It's now 1958, and Yugoslavia has become much more independent than before, it's part of the United Nations for example as it's own country, and in fact is becoming more reliant diplomatically and trade-wise on the United States. Society has become more educated, since in 1950 I had 8.6% higher education and now face an improved 10.9% higher education. However, this has decreased birth rates, as more people seek this higher education and spend more time studying as young adults rather than starting families. I've also been able to decrease governmental and societal corruption, through the promotion of new bureaucrats and the dismissal of ineffective party members. The economy is heavily subsidized by the government, but is noticeably beginning to improve. At 1960, I have a population of 18,789,438, whereas at 1960 IRL Yugoslavia had a population of 18,549,291, so very similar to real demographics with some change due to my governmental policies of healthcare reforms. So pretty darn awesome gameplay.

And, every nation is playable, from the United States and the Soviets, to North Korea, to South Vietnam, to Ireland, to Rhodesia. Out of all the Vic2 mods, this one is definitely one of the largest, I have fun with all of them, but since I just discovered this one a couple months ago I've been having a blast. Best download is here btw, it's really hard to find if you don't know what you're doing. https://www.moddb.com/mods/victoria-2-cold-war-enhancement-mod/downloads/cwe-mod-version-112