Since you asked for actual studies, I think a study on general ankle support in sports will be helpful (It focuses on basketball and volleyball, but has also some generic information that might be useful): Here is a study on ankle support in general.
One should note that hiking does not seem to be affected by that much ankle injuries in general, as mentioned after the abstract:
[...] Some sports like basketball and volleyball
have high ground reaction forces when players
land from a high jump, which accentuates the
sprain and the rate of injury. This accounts for
these sports having 79% and 87% of inversion
sprains respectively and 2.5 times more ankle
injuries than walking or hiking. [...]
On injury prevention:
[...] As has already been mentioned, although some
limitation of ankle range of movement can be
achieved with taping and bracing, it is doubtful
whether tapes and braces will withstand the
forces of an inversion sprain [...]
From the summary:
[...] that both mechanical
and functional stability of the ankle
can be improved with taping [...]
[...] Both taping
and braces have been shown to prevent
ankle sprains in basketball and soccer players, [...]
And the key points:
- Restrict range of movement
- Reduce reinjury rate
- Improve proprioception
- Limitation of movement is lost after exercise
- No negative effect on most performance tests
- Little negative effect on other joints
Summa sumarum, what I gained from reading this paper:
Ankle support does indeed help - so I guess high boots will indeed help too. But: If you have healthy ankles the differences might not be significant.
When the ankles are already instable support seems to be desirable.
I recommend reading over the paper on your own to gain a better picture.
* Disclamer: This patent does not link to any research that confirms the following statements, take them with a grain of salt.*
In further research I stumbled upon the following patent.
[...] The sole is so configured that the boot can be defined to hold the wearer's ankle substantially more firmly than has heretofore been possible. The sole is so shaped that the sole configuration itself effectively performs the rolling action, both on initial contact and on take-off from a step or stride, which would otherwise require flexing of the ankle and foot muscles during normal walking. Thus, the present sole makes it possible to construct a hiking boot which has substantially improved performance in terms of protecting the wearer from fatigue and injury while walking long distances over various terrains. [...]
The text above basically states that with this sole less ankle movement is required, therefore reducing the risk of fatigue and therefore injury:
[...] holding the hold the wearer's ankle substantially more firmly [...]
Where we get to the "the force needs to move somewhere else topic (knee)" which is not evaluated, as so often.
The US army performed a test on hiking boots in 1999 - quite an interesting read, but with no real value besides that high top boots have different effects on ankles too.
The Asolo AFX 535 (boot 10) scored very well as to perceived comfort, prevention
of slipping, and rate of oxygen consumption during unloaded walking. It performed
poorly at preventing foot or ankle pain [...]
The study also considered
[...] shielding the foot from rocks and stones [...]
which is obviously a factor if you want to compare high top vs low top boots. It has a slight impact on ankle injuries that could be prevented by higher boots, so you might want to factor that in for further research.