Upside-down Fork vs Traditional Fork
The unsprung weight thing is a myth for the most part.  Cast aluminum and magnesium lowers are extremely light, for example, old marzocchi 66 ones were only 3/4 of a pound, total weight.  It's not as if the stanchions, dropouts, lower-internals and anything other parts are weightless on an inverted fork, then you have to compare the weight difference with the unsprung weight of the fork, axle, brake rotor, caliper, rim, tire, spokes, etc.  In the end, it ends up being significantly less than a 10% difference and a tire-change would have a much bigger effect.  

The lubrication is about the only valid benefit, as you get better lubrication with an inverted semi or open-bath design.  The tradeoff is if the seal fails, the fork drenches your brake in oil, which would leave you without a front brake.

Fore-aft stiffness is better as the fork progresses through travel, but here's the big issue with this, to make an inverted fork, even a dual crown version, as torsionally stiff as a non-inverted fork, it needs a lot of reinforcement.  To date, no one has really accomplished this and even less-so with the single-crown versions, which have no 2nd crown to help out with the twisting forces.  So, the inverted designs end up weighing more, and with your non-inverted design, you could simply use bigger stanchions, as Fox has done with forks like the 40, and go right back to having as good or better fore-aft stiffness.  Other modern additions like 1.5 steerer tubes have also boosted fore-aft stiffness significantly.  So for motorcycles, which don't have a brake-arch on inverted OR non-inverted designs (we'll get to that), where casing the jump at 60mph is a real concern, a big heavy inverted fork is great, but it's not apples to apples with mtbs and with the forks always ending up heavier, you can simply use bigger stanchions on a non-inverted mtb fork.

When the travel gets long enough, you do have to go to an inverted design to get the proper bushing overlap, so more than 8" or so, it usually makes sense to go inverted to avoid crazy extended lowers that extend below the dropouts.  This is one big reason why modern MX bikes use inverted designs.

Other reasons it's not apples to apples for say road-going motorcycles is that something like a sport-bike will have around 3" of travel and huge stanchions and bushing overlap.  It'd be like running a dual crown mtb inverted DH fork with only 2" or 1" of travel, which would be easier to manage in terms of making it stiffer.  Another big reason it's not the same thing is that the off-road and on-road motorcycles rely on the huge beefy crowns and material in the uppers between the crowns.  These forks will often have no steerer of any kind, only a rod that is used to preload the bearings, obviously mountain bikes are quite difference functionally in terms of design, so the crowns are significantly weaker and will allow a lot more torsional flex.

Inverted forks do look cool, but to make them anywhere near as stiff as conventional ones, it requires exotic engineering or exotic materials or a combination of both.  This means things like keyed stanchions, or carbon-fiber upper structures, etc., and in the end, if you spent that time and energy on a conventional fork, you'd still beat the intverted in terms of weight and rigidity.  I've owned many inverted forks, single and double crown.  The lack of torsional rigidity is real and in some cases pretty scary.  Better designs have minimized this, but there's little reason to actually seek out an inverted design, as there's no real benefit or advantage, except in some extremely limited situations (like you need a 10" travel fork for some reason).