I had two thoughts:
1: Distribute the weight across more wheels, kind of like tracked vehicles do. Maybe good for tracks that were built on poor footings or with rotten ties/sleepers.
2: Improve traction. Normally each wheel has one point of contact with the tracks. This way each drive wheel has two points of contact (one with each of the first-tier extra wheels) and each of the first-tier wheels has two-points of contact with the second-tier extra wheels (not sure what else to call them).
I guess in that respect I don't understand the Hollman Horror's websites criticism of the thing. It claims that more wheel-wheel interface would creat more slippage. I would think the opposite to be true - more surface area contact would reduce slippage.
I would guess that they were thinking along with one or both of those ideas, but were probably wrong. It would be overly complicated and top heavy.
It's an interesting idea, and one can conceive of it having been the reason, but I'm not sure it works, as a component of wheel slippage is weight distribution. In other words, though the surface area of many little wheels might be marginally greater than that of one big one, the pressure is also reduced. Add to that that much of the slippage will occur at interfaces other than the wheel to track, and that the mechanism will dissipate a lot of potential energy, and if there were any slight advantage it would likely disappear in the implementation. At a given speed, small wheels will also spin much faster, and I suspect wear would become more of a factor.
A tracked vehicle is not necessarily the best example. A tracked vehicle is actually a track
laying vehicle, properly speaking, and what it does is to lay down at one end, and pick up at the other, a cleated or high traction track which is designed specifically not to roll, over which the internal rollers then roll. Ideally, the track does not move against the surface at all, and as a result it can be as knotty and gnarly and un-rollable as the surface it travels over allows.
I haven't studied the engineering of this at any length, and this is certainly a thread divergence if not derailment, so one must leave it there despite its being in some ways more interesting than voodoo physics. But I suspect that the Holman Horror might have been, in part, a sincere effort based on bad theory. If the basic idea of many small wheels on the track had merit, it could have been done, I think, by gearing rather than by multiplication of wheels. Of course the history of fraud is varied, but the fact that actual locomotives were made suggests pie in the sky engineering more than scamming here.