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Fighting even a one-front war against a major adversary (Russia or China) would require mobilization--and it would have at any time during the Cold War, too. We used to maintain a more significant defensive posture: e.g., in the Fulda Gap to prevent the Reds from pouring through Germany, and on the DMZ in Korea, to prevent the insane leaders of North Korea from being too insane. But realistically, that's not our current threat, and it doesn't make much sense to maintain that kind of defensive force. And even those defensive forces were never going to be enough to win the war. In Korea--the one I know more about because I was there--we were there to give our mainland forces a month to deploy. That was it: our goal was to survive for a month. (Also, the South Korean's military was generally more than 10x as large as our forces there). I suspect that is still the goal.

I want to add this:
The presence of about 25k US troops in S. Korea is no doubt partially for the tactical, on the ground reasons that you give but I think that ultimately the bigger reason is a more macro-level global-political reason:

Going back 74 years to the Korean War, it arguably started because Dean Acheson gave a speech on January 12, 1950 in which he defined a US "defense perimeter" running from the Ryukyu Islands (Japan) to the Philippines.  This notably does NOT include the Korean Peninsula nor Formosa/Taiwan/Republic of China. 

Acheson bitterly defended his statement and people have been arguing for going on three-quarters of a century as to how much impact it had but the facts are:

• The text of Acheson's speech was examined by Stalin.  
• Prior to Acheson's speech Stalin had rejected numerous plans from Kim to attack S. Korea.  
• A couple weeks after Acheson's speech, Stalin gave Kim the green light. 

This brings me back to Korea today.  The 25k US troops on the DMZ are there, IMHO, more than anything else to make an unequivocal statement to Kim, Putin, and Xi Jinping that the US absolutely will fight to defend S. Korea. 

Their presence on the DMZ makes it impossible for N. Korea to attack S. Korea without engaging US Troops and causing US casualties.  It is possible that Kim is so batshit crazy that he doesn't understand this, but Kim can't attack S. Korea without, at an absolute minimum, logistical support from China and/or Russia.  Xi Jinping and Putin absolutely understand the presence of US Troops on the DMZ as an unwavering US commitment to the defense of S. Korea. 

So I agree with you that IN THE EVENT OF A WAR, the job of the ~25k US Troops in S. Korea is to "survive for a month" so that mainland US Forces can be deployed, but the MUCH more important function of those ~25k troops is to prevent that war from happening in the first place simply by being in a position such that the N. Koreans can't invade S. Korea without engaging them and killing some of them and thus (essentially) automatically triggering a US Response. 

Does the South have nukes?

Currently, our military is populated with a historically large (not the biggest) number of combat veterans. That's useful, but they aren't veterans of the kinds of wars we're talking about. They are really good at clearing and holding cities from insurgents, but major force-on-force fighting isn't something we've done, really since Korea in the 50s. Even in Vietnam, we were primarily fighting light infantry battles, ordinarily not against a well-organized, state actor. We've trained on it a lot--and we still do--but another thing that is rapidly changing is the impact of surveillance and remote warfare on the battlefield. That's a big reason for everything bogging down in Ukraine. It is very difficult to mass for attacks without the enemy knowing what you are doing, and defending against it with remote actors: drones, artillery, and other long-range strike capability.

I've read a lot of military history and what concerns me is that we really don't know where this new technology will take us.  

Example:
Most people think of WWII Germany and they immediately think "Blitzkrieg" and "tanks".  Thus, they assume that Germany was able to overrun France so quickly in 1940 because Germany had:

• Really good tanks, and
• A lot of tanks, and
• More tanks than France.  

None of of those things are true.  The German tanks circa 1940 were good but not great and the French tanks were arguably better.  What is unarguable is that the Germans absolutely did NOT have a lot of tanks in 1940 (at least by later war standards), and that the Germans had LESS tanks in 1940 than the French.  

Anyone unaware of those things is probably wondering, "Ok @medinabuckeye1 , if German tanks in 1940 weren't all that great and they didn't have all that many of them and they had less tanks than France, then how did they overrun France so quickly?"  

The answer is superior doctrine.  This seems obvious in retrospect and by mid-war everyone understood it but the Germans were the first to figure out that the most effective way to deploy tanks was to mass them and use them to smash through weak points in the enemy's line then encircle and destroy large enemy formations from behind.  By 1943 this is what everyone was trying to do (see, for example, the Russian attack at Stalingrad in late 1942/early 1943).  However, just a few years earlier in 1940 this was a completely untested idea.  Most everyone else including especially the French viewed tanks as "infantry support" rather than a stand-alone weapon system.  Thus, French tanks were scattered along the front.  The French has more overall but where the Germans chose to attack they had a LOT more because they massed them and smashed through a weak spot.  

Similarly the Japanese attack on Pearl Harbor was such a stunning (tactical) success because it was the first use of a truly large scale mass of Aircraft Carriers.  Even the British success at Taranto was with only (IIRC) two carriers.  The Japanese sent six carriers to attack Pearl Harbor and, at the time, that was the largest grouping of carriers that had EVER been deployed.  Some admirals in other navies had been arguing for this approach but the older, 'battleship admirals" saw Aircraft Carriers much like the French Generals saw Tanks.  They viewed the Battleship as paramount and the Carrier as something of a "battleship support weapon".  

Everyone in 1939 knew about tanks and carriers.  Both had been around since the end of WWI but the late WWI tanks and carriers were first generation weapons that weren't very good.  The tanks of 1918 were notoriously unreliable and not very well armored and the carriers of 1918 were miniscule rebuilds of other ships that carried a few primitive aircraft that more closely resembled the Wright flier than a modern plane.  By 1939/40 tanks were modern, reliable, and well armored.  Carriers were humongous and carried up to almost 100 all metal, single-wing, 350+ MPH planes.  

The powers that were the most successful in 1939/40 weren't always the powers that had the most, they were the powers that deployed theirs most effectively.  

This concerns me because we don't yet KNOW what the best methods of waging war will be in a world with A2/AD, drones, surveillance, remote warfare, etc.  We can speculate but until a major war is fought we don't actually KNOW.  

AFAIK, S. Korea is not an acknowledged nuclear power.  However, they are sufficiently technologically advanced that they have to be considered at least "nuclear capable".  That actually is probably another reason for the presence of those aforementioned ~25k US Troops on the DMZ.  So long as they are there, the S. Koreans are probably willing to forgo becoming a nuclear power because they can be confident that the US will assist in their defense if they are attacked.  If the US Troops were removed, S. Korea would be MUCH more likely to decide that they needed a nuclear deterrent to protect themselves from N. Korea. 

Pretty sure the South does not have its own nuclear arsenal. They have us for that. The North's arsenal is a deterrent to agression against it, but its use virtually guarantees the North's annihilation. After Iraq, 2003, it's unsurprising that it, Iran, and other simililarly situated nations would want a nuclear arsenal of their own. NK was already working on it, but guaranteed that they sped things up after that.

The Second Infantry Division in South Korea is viewed as a "trip wire", as noted above.  It means if the North attacks, there is no doubt the US would be immediately involved, which one presumes hinders the north.  I mentioned before visiting the DMZ there, it is a strange experience.  That war technically is still happening.

The South would dearly love to recombine even though it would cost them billions upon billions at first.  The South has something like 600,000 soldiers under arms, the North has about a million.  The US Second ID has about 20,000.

I assume you are getting you taxes rebated for you off the road vehicles.

We show gas as an expense in our books.

Of what?