Plants, like every other living thing, specialize for environments. Propagation is how they test their specialization pressures. That testing tends to happen over hundreds of thousands to millions of years.
Shipping mature adult plants around the world to different climates is not the same thing as the kind of seasonal, glacial changes in specialization that they are adapted for.
> Everything I have learned about seeds tells me that plants try their damndest to spread their DNA as far and wide as possible.
This seems no less true of animals, many of which go so far as to move their entire body considerable distances to find food, mates, and suitable places to have offspring.
Everything I have learned about seeds tells me that plants try their damndest to spread their DNA as far and wide as possible.
In a sense, flying live plants all across the world is exactly what they're hoping/living/existing for.