This is a linkpost for https://maxniederman.com/posts/conventional-military/
"There are many animals which have what are called dominance contests. They rush at each other with horns - trying to knock each other down, not gore each other. They fight with their paws - with claws sheathed. But why with their claws sheathed? Surely, if they used their claws, they would stand a better chance of winning? But then their enemy might unsheathe their claws as well, and instead of resolving the dominance contest with a winner and a loser, both of them might be severely hurt." -Professor Quirell
Or to be more explicit, anything less than total war is a dominance contest between factions, not a no-holds-barred attempt to win. Nuclear weapons are useful for deterrence, but if there is a situation in which neither side is willing to simply back down, but both also want to limit the destruction, then a conventional military becomes very helpful.
In the practical art of war, the best thing of all is to take the enemy's country whole and intact; to shatter and destroy it is not so good. So, too, it is better to recapture an army entire than to destroy it, to capture a regiment, a detachment or a company entire than to destroy them.
One cannot use nuclear weapons to take and hold territory.
You also say:
Conventional military is entirely useless except for proxy wars and small-scale meddling in non-nuclear states’ affairs (e.g. the Vietnam or Afghanistan wars).
But another way to say that is:
“Conventional military is useful for proxy wars and small-scale meddling in non-nuclear states’ affairs.”
The United States does these things quite often.
In 1950 as part of the Korean war, China attacked a force under the banner of the UN, but consisting mostly of US and South-Korean soldiers even though China did not have nukes (and would not have them till 1967) and the US did.
So, one reason to have a conventional military is that nukes aren't enough to prevent even non-nuclear states from attacking you. Well, yeah, you could say that if the US didn't have a conventional military to send to Korea, then there would've been no US citizens within range for China to attack, but then the US would've had to put up with South Korea's being absorbed by North Korea and consequently becoming communist. (And if that happened and the US Navy was incapable of projecting non-nuclear force, Taiwan would've been the next to fall.)
Given what actually did happen during the Korean War (namely, China's not being afraid to kill many thousands of US citizens in the process of preventing a takeover by the UN of North Korea followed immediately by China's strenuously trying to take over South Korea), if the US hadn't sent a conventional military force to Korea, but merely announced to China and North Korea, "We have nukes, you do not, so don't you dare attack South Korea because if you do, we will nuke you!", that announcement or threat would not have been enough to prevent some combination of China and North Korea from taking over South Korea.
I could not find an estimate of US casualties inflicted by China for the entire war, but in the so-called "second-phase offensive", described in the first paragraph of this next page as "an offensive by the Chinese People's Volunteer Army (PVA) against United Nations Command (U.S./UN) forces, most of which were soldiers of South Korea and the United States", China inflicted "24,000 casualties (including 4,538 killed)" on the US military.
https://en.wikipedia.org/wiki/Second_Phase_Offensive
I picked the second-phase offensive at random: China mounted 5 of these "phase offensives".
World superpowers, particularly the United States, still maintain large conventional militaries despite nuclear deterrence. Why?
In order to conduct non-nuclear forms of war, with aims such as regime change, peacekeeping, counterinsurgency, and defense of allies.
Russia has directly threatened nuclear retaliation against the US if it were to send troops to Ukraine, and the US military remains largely useless.
However, USA sends weapons to Ukraine. Weapons are also a part of military spending.
This is true, but it doesn’t answer the question of why not to simply use nuclear blackmail on such states. And the answer to that is that the US wants to limit the destruction of war. Nuclear blackmail is great, right up until someone calls your bluff. But then it helps to have conventional forces if you do not wish to have massive losses to local civilians, local infrastructure, and one’s own prestige.
The main reason USA (and other nuclear powers) don't use nuclear blackmail is that it would end no-nuclear-proliferation regime. "Every state that can make nukes has them" is the natural word state, keeping non-proliferation requires effort.
Most people agree that the United States spends far too much money on its military. Spending more than the next ten countries combined is obviously overkill. But what truly baffles me about the United States' military spending is how much of it goes to conventional military.
Conventional military is entirely useless except for proxy wars and small-scale meddling in non-nuclear states' affairs (e.g. the Vietnam or Afghanistan wars). If the US or another state were to use their conventional military to attack a nuclear state, they would be subject to the threat of nuclear retaliation; i.e. mutually assured destruction applies not only to nuclear aggression, but also to conventional aggression.
Of course, an attacking power might decide to call the defender's bluff by taking only a small amount of territory, but this is very risky and a line must be drawn somewhere to avoid escalation. In the Cold War, we saw this line drawn inbetween proxy wars and direct attacks on enemy territory. If anything, the threshold has become even lower since then; Russia has directly threatened nuclear retaliation against the US if it were to send troops to Ukraine, and the US military remains largely useless.
The usual explanation for why the US wastes so much on its military is that the incentives of defense contractors, the Department of Defense, and Congress are all aligned to increase military spending, even to the detriment of the citizens. This makes sense for military spending in general, but I don't see why they would spend so much on conventional military; why not just spend it on nuclear weapons and defense research?