A mountain bike (and anything related to its, like the wretched short-arse Gunnar that Paramount makes), as Ridealot intimates, is the wrong sort of bike from which to expect stability. Its designer had deliberately made it quick to change direction, and therefore unrelacking to ride. What you want, if stability is your measure of goodness, is a bike which for a start has a longer wheelbase, an understeering geometry (that's a low head- and seat-tube angle like 68 degrees rather than a higher one like 72 degrees to go with the long wheelbase with a medium to long trail), no careless barbelling bits haphazardly arranged on the handlebars, fat tyres rather than thin, your seat well inside the wheelbase (none of these modern short-arse bikes with the saddle hung out almost over the rear hub will do), and so on. I have such a stable bike, capable of being ridden hands-off at speed through potholes. You can see it at
http://coolmainpress.com/AndreJute'sUtopiaKranich.pdf
Compare it to the other bikes on my bicycle page at
http://coolmainpress.com/BICYCLING.html
and you'll soon that it is a very different from them in almost every respect beyond having two wheels. The downside of such a bike is that many would consider it slow-handling but in fact on the downhill parts of my very poor roads nobody has ever passed me and those who try to keep up end the day with white brackets around their lips and knuckles whereas I don't even notice the road is bad; it's like having my old Bentley Turbo back, a steamroller on two wheels.
If you want to build a stable bike you can't start with mountainbike frame, and generally speaking most popular frames have too many insuperable difficulties, almost always starting with too short a wheelbase. So you have to design and commission a custom frame, pay for a semi-custom frame from Europeans who have designed touring bikes from the ground up (there are a few Americans too, but I suspect them of crept-in 10-speed influences); that leaves you at the pricey end of the market, with Utopia (my guys, known as the Rolls-Royce of Bicycles for many good reasons), Patria, Thorn and from there the prices hike north rather suddenly because now you're into one-offs.
Before you start looking into custome bikes, here's a simple question for you: where will you get double-butted bicycle-weight tubes long enough for this notional bicycle of yours? (Hint: the tubes on my bike were specially drawn by Columbus in Italy, the same people who draw pipes for Ferrari. Ask yourself what that will cost for a one-off.)
The smart alternative is to find an old Raleigh tourer frame, forget that it is a venerable antique, and get someone like Muzi to modernize it for you so it takes modern components (bottom bracket, headset, frame- and fork-ends, bracketry) and, most important, to spread the forks for you so that you can fit minimum 50mm tyres, preferably 60mm low pressure Big Apples. (Or maybe Muzi can somehow make that Indian Raleigh copy that he sells into a lasting, smart proposition with a bit of Waxoyl and paint.
Anyway, a stable bike isn't impossible, but it will be long, it will definitely be clumsier than a road bike or a mountain bike, if you want to ride it fast you will have to learn new skills (if you're into big, fast transcontinental tourers you already have four-wheel skills and attitudes that transfer whole). On the other hand, my big stable bike is in fact the cheapest bike I ever owned. The tyres aren't worn out yet at over 8000km (and anyway, Big Apples are cheap), and the rest of the maintenance is new oil for the hub gearbox once a year, less than twenty dollars for the entire kit, plus a shot of Teflon grease once a year. That's it for seven years now. The brake blocks are still good too. A stable bike will almost by definition be a big bike, with more of everything to spread your weight, and the wear, across.
So, no, the lack of hands-off stability isn't a plot, it isn't even deliberate, it just happened for other reason.
If you're in reflective mood, you could consider that the most stable bike you ever owned or rode was probably a beach cruiser, the first of the fat bikes of which the Big Apple tyres I consider so stable are the direct inheritor. Those first beach bikes also gave birth to the mountainbike craze...
Andre Jute
What goes round comes round