Just my tuppence,
The original idea of dovetailed infill planes was to eliminate casting stresses that are found in Stanley type planes. When metal is cast it contains stresses that, over time, even out. This warps the plane, meaning that it needs to be flattened.
Dovetailing flat pieces of steel together means that no stresses are formed (this is a slightly touchy subject, some argue that stresses are still there, albeit far less than the cast counterpart).
These U-shaped dovetailed sections can then be made into planes, and infill is the decided upon option.
Thus, infill planes should never need to be flattened!
Now, that said, old USA Stanley planes and equivalent have had enough time that the stresses should have pretty much come out, so a flattened USA plane should stay flat. (This can also be seen in chisels, and is why modern chisels are thicker than old ones, but that's another story)
I think, more than anything, that the reason why infill planes are popular now with collectors and the like, is that they represent the finest craftsmanship of toolmaking. Sheffield, at its height, was producing arguably the finest tools in the world, and the infill plane is seen as the pinnacle of that achievement.
In terms of practical usage, they work. They work very well, but arguably no better than a Stanley plane of the same vintage.
All the above said, please take what I say with a pinch of salt, I'm no expert!
Fraser