Hi Steven
Your question prompted me to give this some serious thought, I own two custom bikes (touring and randonneuring) and I have to say it really depends on your personal perspective. 
I have ridden many bicycles over the years and there are distinct differences when comparing higher end bikes with off the shelf varieties.
Even as a young and beginning touring rider I found myself modifying stock bikes to become more suitable for the riding I did....swapping double cranks to triple, building my own wheels attempting to reduce spoke breakage, fiddling with different styles of brakes, enduring many types of tortuous saddles until settling on leather Brooks touring saddles, realizing that micro-adjustable seat posts were better for me due to my sensitivity to seat angles resulting in numbness... I think you can see where I am going with this.
Will a stock bike get the job done, absolutely and quite well if you consider for instance the large number of reportedly happy riders of Surly LHT bikes out there.
There are good reasons that higher end components cost more.
If you are a bike tinkerer like myself you quickly discover the quality differences in hubs, brakes, cranksets, bottom brackets, derailleurs, etc.
Even a component as lowly as spokes will show a broad range in quality of manufacture. Better components work better and last longer, it is a fact.
They also cost more. 
A somewhat recent phenomena in the bicycle manufacturing world is the shift of attention toward more versatile bicycles, the wider tire gravel bikes and rando style bikes we are beginning to see from mainstream bicycle companies were mainly driven by the custom builders and riders of these bikes themselves and not the racing dominated industry.  Riders discovered these bikes were more comfortable and just plain fun to ride and they began to chase down and modify appropriate vintage components if available or even develop their own components that are more suitable for the style of riding they enjoy. (Compass Cycles and Velo Orange are two very good examples of this trend.)
Another factor is the broad based and ever accelerating electronic technology based gadgets that are so much a part of modern daily life.  When I began riding bikes in the early 70's there were no such thing as internet connected smart phones or GPS or LED lighting. The incorporation of these technologies into the world of bicycle riding and touring has dramatically changed (and I think improved) our sport and passion.
We can now with the help of a decent dynamo hub front wheel and/or solar panel charge our various electronic helper gadgets as we ride, reducing or even eliminating our reliance on outside power sources.
The addition of these technologies to a touring bike is relegated to the motivated tinkerer to do himself or herself, or to the custom builder to integrate into a unified design that may include custom racks and internal wiring that is practical and elegant as well as aesthetically pleasing .

Of course all of these things cost more than a stock bike with stock components, it is simply a fact of life.
It really boils down to what kind of riding you do and how important these extras may or may not be to you.
I can only say that when I finished the build and rode my new rando bike for the first time last spring I was thrilled with the result, a smooth as silk and versatile bike that makes me happy every time I ride it...absolutely worth every penny.

Best,
Randy R

Oooooooh, Yeaaaaaaah.  I forgot about saddles!  I will pay just about anything for a comfortable saddle.

;-D

I rode a Surly LHT for about eight years before acquiring my Thorn Mercury.

When I bought the bike the LBS provided a bike fit as part of the cost of the bike. This took about three hours over two visits to the shop. I was very comfortable on that bike. And I was even more comfortable when I swapped the cantis for V brakes.

Mike

I agree with many of the common threads coming out of the previous posts, a few differences for me:

• With a skilled fitting, I found standard frames can be matched to my physical parameters and riding style. I weigh 230 lbs, have never had a standard frame break or in any way fail on a tour - as long as it is a major brand and has all the braze-ons I want, not much different there for me.  Though, over the years I have to admit: some frames just look cooler than others and I'll open my wallet a bit further!
• Wheels are worth spending extra on. Essentially, strength to weight is key. The first bike I did multi-day rides on was a Schwinn hybrid that began to break spokes on the rear. Tried replacing that with 32 spoke, triple cross off the shelf wheel, still broke spokes. Local bike shop hand-built a wheel for me that never broke a spoke in years of riding. I bought a new road bike last year, pretty much chose it based on the wheels.
• No one ever stays with the saddle that came on the bike - worth spending more there.
• Components - I really can't tell much difference there between the typical levels, though over the years they have all certainly gotten better. The weight savings moving up is a trivial percentage of my body weight, the shifting doesn't seem much different, reliability seems about the same, though lighter weight can actually mean lower reliability.
• Pedals - probably again a function of weighing 230 lbs, I have found more expensive pedals to be more reliable.
• Tires and tubes - I used to be a real cheapy, buying low end stuff and getting really good at fast repairs on the road. I joined the Schwalbe bandwagon, now spend much more on tires and spend more time after each ride checking for debris in the rubber - and go years between flats.
• Bar tape - this was the last area I moved upscale on. The new road bike I bought came with really cushy  foam bar tape - I loved it. Put it on my Trek 520 touring bike even though it cost twice as much as what I would typically put on!
• Test ride - before you pick a spending level, ride a few at different levels and see what calls to you. Personally,  I am not able to tell the difference between a "lively" or a "twitchy" bike or a bike "that wants to climb heavily loaded." All the adjectives used in commercial bike reviews seem like they had a seance with the bike, vs. anything I've ever felt.  But, get on on one and ride for a few miles and I can tell whether it is right for me or not.

Nice detailed explanation. I haven't had any major issues on tour yet (knock on wood), but I can see how difficult it would be trying to replace a tire when you didn't think you'd need to. Tires seem like one of those things where getting something substantially better doesn't cost all that much more -- at least compared to some other kinds of components. I'll look into the Marathon Supremes before my next long ride.

I've always rolled with whatever wheels came with my bike when I got it, but I accept that I might just be a lucky guy that nothing too bad has happened yet. I'm not sure I ride long enough or often enough to splash out for a Rohloff hub, but Chris's journal where everyone is running into broken spokes makes it seem like a good wheel truing would be $$$ well spent.

Thank you for taking the time to write such a detailed post. It's really good to read the "why" behind the decision to get something that's custom to you. I probably won't be able to do that for awhile, but do you feel like there's value in getting a proper bike fitting so that I could at least make adjustments to what I already have? Or is there only so much one can do if the bike itself isn't quite the right size to begin with?

Happy to hear that the new bike works and feels exactly as you hoped it would. I don't know all that much about why one type of part is better than another (not yet anyway), but one thing I like about bikes is that you can mess around little by little for cheap, learn about how the different parts work -- and if you don't like whatever change you made, it's not hard to undo it. I think I'll have to get more into all that stuff this year.

"No one ever stays with the saddle that came on the bike" -- well, almost no one. I have so far. But I'd never really gone long distances before I bought the bike I have right now, so I guess I don't know the difference!

Same goes for bar tape. I never thought that could make a difference, but then I guess it makes sense when you think about how you're spending four to ten hours a day leaning into your hadnlebar.

Anyway, this is all helpful stuff to think about. Thank you for sharing all  your thoughts.

Steven,
It is my sickness and addiction, the bike tinkering thing.
Be careful if you dabble with it, you can be ensnared before you know it and the next thing you know you become the dreaded and much despised "Bike Snob"  ;-)

Joking aside one point I was (poorly perhaps) trying to make about bike mods is that It doesn't take that many new components to add up to a significant sum of money.
At that point a custom build that gets you where you really want to be in one fell swoop starts to look a little less indulgent and perhaps more reasonable cost-wise.
RR