There are costs being here, but, first it's not that much compared to our GDP. We're also drawing down, as we were 130k at peak and we're now under 90k troops. Second, it's an NATO-ISAF mission, so the US isn't paying for all of it. We pay a majority, but not all of it. Let's look at it historically. We stayed in Iraq and although sectarian violence is a growing problem, they are governing themselves and no longer a threat to the region. We stayed in Japan, and they became, within 20 years, the leading country in terms of manufacturing and economics (as a result). In the 70s and early 80s, Japanese cars were derided in the US and quality was lacking. Today, a Japanese car (Honda, etc) holds a better resell than many domestics and the quality is top notch. Compare that to Hyundai. I had a Hyundai XG350 listed for $2,000 under value for a year and only got one call. We stayed in Germany, and within 20 years they became a powerhouse within Europe. Today, they keep the Euro afloat and have the largest, strongest economy. On the flip side, we ran from Vietnam and 4 decades later it's still stagnant. We ran from Mogadishu, and tens, if not hundreds, of thousands are slaughtered annually. So the answer to your first question is: It depends. There was a political will in Europe, and Japan, and we're still in those regions today with Air Force and Army bases that foster information sharing, Joint/Combined military exercises, etc. If we punch out due to a lack of will to see this through, then the historical answer is that someone, not us, will prevail. It could be the Taliban, China or Iran, or some other power sharing. On your second question, the Taliban does cost money. Their fighters expect to get paid, you have to buy the chemicals they use to make home-brewed IEDs, and logistics. They're hurting big time because not only are we killing their leadership (who know where the money is), we're disrupting their ability to move and use cash. Like I replied earlier, there are a lot of foreign figthers. You have to equip them, move them, etc. So just as they try to disrupt our "Freedom of Movement," we restrict theirs so it costs more to train (locations move), costs more to equip (we are raiding their caches in staggering numbers), and move the cash (there's corruption on their side too... $10 sent might result in $1 making it).
On your second paragraph/point, you might be right. We will see.
The third area it's harder for me to gauge where we are, versus where we were, and how effective things are in making things better. Under Gen McChrystal and Petraeus, the daily CUA (briefs to the senior leadership) had a lot of status slides on rebuilding, training, local governance, population outlook, etc. The new 4* General is a USMC guy, and he doesn't appear to be embracing the "hearts and minds," campaign they created, called COIN. It seems he's gone more into Special Ops, and just plain punching the bad guys straight in the face (to use a euphemism). He's also adopted a more "Obama style" approach of keeping the exit door in view, but that may just be a coincidence. I don't think it is, but it's possible. We're due to draw down in 2014, and Obama has shown that regardless of a power vacuum or other problems left behind, he just wants out. Two years ago the ANA was hardly ready to take the lead on any operations, however, I've noticed that lately they are taking the lead quite often and actually doing very well. They're effective at calling in Close Air Support (harder than it may seem), basic searching and security, etc. It's now quite common to see successful operations they performed alone, as well as Combined patrols where they took the lead. Maybe one day if I have time, I can look at this from a Macro view and see how spread out they are, but I just haven't had the time and it's not part of the briefs I see. My main takeaway on this point is that we're training more of them, they're getting quite effective, however they have large logistical and public perception issues in some areas.
If there's any thing the US is insanely effective at, it is logistics. Pakistan, Iran, China, and Russia could all cut us off, and there's never going to be a problem with supplies. We've gotten so effective at air drops, we'll actually do it to move stuff across a couple hundred miles, when previously we'd use a truck. It's partly because it really frustrates their IED intentions when we stop driving regular routes with supplies, but also because with disposable parachutes that are GPS guided, with much cheaper guidance systems, air drops have gotten insanely easy to be effective for routine resupply. Remember, Russia completely blocked off West Germany, and we had no issues overcoming this with military airlift. To be really honest, the Pakistan blockades only impacts us weenies who enjoy getting Snicker's bars from the local shops (just as one small example). It's actually a good thing since I'm trying to drop pounds. :) So to your very last comment, logistics is never a problem. You see how fast we pulled out of Iraq? No small feat, but executed with high effieciency.
I know the whole, "US economy will collapse," is popular right now, as one can also say the European economy is the same. However, it's not because of the war. We're on the downward slope from a 2 year peak in ops, and the cost is estimated around $1.5 trillion. I don't agree with the $1.5T, but it's the worst number I could find, to give your argument the strongest supporting figure. The US GDP was over $15T (estimated) for 2011. As we draw down both in Afghanistan, as well as the standing military forces, and go into 2012 with no Iraq military presence, the cost will drop to a large degree, with current estmates indicating 33% of those costs, or around $500B. The Army, Navy, and USMC are sending thousands home. By home, I mean, out of the military, thank you for your service. The only reason the Air Force isn't is because they were ahead of the curve and already cut the numbers they needed to trim in 2011/early 2012. So if our economy fails, it won't very likely be spending on military that's under 4% of the GDP. It will more likely be due to Obama-care, Medicare, and the debt service from long-running deficits in government programs (not including military).
A great deal of inflation is due to too much money chasing too few goods, and/or public perceptions. Since unemployment is still higher than what I think everyone would agree is a sustainable, healthy percentage (7% give or take), and Monetary Policy is still holding lending rates low (a few percent), there's not too much money "out there" (chasing too few goods, or "scarcity"), nor a high cost to get capital/cash. Also, people's perceptions seem evenly keeled, except for short term energy costs. It's no coincidence in my mind that since gasoline and other energy costs dipped just a bit before Christmas, that spending increased for the shopping holidays. Similarly, people didn't expect to pay more for the same goods. Meaning, there was no consumer perception of an expected inflationary pressure on prices. I don't know if you were sincere or jokingly exaggerating, but even with as horribly wrong as Europe and the US has had it, only Brazil in recent history has gotten to the point of hyperinflation. If we get out, it won't be because of fiscal reasons, and if we collapse financially, it won't be greatly influenced by our military operations.
Karzai's fate took a huge change of course when Mr. Rabbani was assassinted. I think his public demeanor showed how grave this turn was. If things did turn violent when he left, Rabbani was a large ally to have. On the flip side, the way the GIRoA constitution is written, Karzai can't run after 2014 for President. If you read the preceeding article, which contains a trans-continental pipeline issue I haven't really thought about recently, I would have to say secretly Russia wants SOMEONE to be a stable government after we leave. If history has taught us anything about Afghanistan, it wouldn't be the Taliban that you want. They'll be very openly hostile to any Russian interests, among a few other issues created. So after this wall of text, where are we? Good question. I can very well defend either position: They'll descend into chaos after we leave, or, stability may be achievable for the short to medium term (5-50 years) after we leave. And so you may be right about it living up to its reputation. But to be honest, in my opinion, we're really done, and so it'll be their own graveyard. We killed OBL, we kicked the Taliban out of power, we helped rebuild, we trained them, we equipped them, we got them off the sidelines and into the habits of sustainable governance.... If they fail, it won't be from a lack of worldwide efforts to enable them to succeed. You realize over 53 countries have people here trying to help them rebuild? That's just military-related. There are a few countries that will never publicly admit they're here, but they're here too, in an attempt to make Afghanistan a productive part of the world's economic landscape (even if it's to the detriment of US economic interests).