I'd like to challenge this assumption:
And it doesn't look sturdy, either, so of/defense against predators can't be a factor, either.
A fragile horn might be better for defense against predators than a more robust one, if the cost of growing one is marginal. Lizards which have a break-away tail and plants with detachable spikes have similar adaptations.
The unicorn is an equine, so unless there are some very good reasons for a different survival strategy, they're going to be herd animals. In a group defense situation, their default strategy may be similar to the muskox: create a circle with the young on the inside, horns pointing out.
This is already going to deter the majority of predators, as the horn is long enough that they wouldn't be able to get close enough to harm one unicorns without running serious risk of being impaled.
For those that are foolish or desperate enough to make a run at it, the majority of the time they'd be skewered.
In this case, being able to give the horn a bit of a twist and have it break off may be the fastest and easiest way to put distance between the the dying predator and the unicorn it's impaled on. This is desirable for two big reasons:
- Preventing the dying predator from fatally injuring the unicorn it's now attached to is a really good thing for the unicorn.
- Having a corpse decaying on the end of a unicorn horn would be problematic, both from the risk of infection as well as general awkwardness.
This isn't as much of an issue for a species with a smaller horn and more robust frame, as they simply toss the predator off their pointy bits in the same movement with which they impaled the predator. An equine body type is pretty strong, but not well adapted to lifting with the neck, so the evolutionary cost of strengthening the head and neck could very well outweigh the cost of producing a long and thin horn.
A whitetail deer can grow up to 200 inches of robust antler over 120 days. We can approximate the shape of the antler by assuming that the thick and thin bits even out and it's basically a cylinder. The circumference of that cylinder we'll ballpark at about 4.5 inches. Based on those values, we get 322.29 cubic inches total and a growth rate of 1.6 cubic inches per day, which we'll round down to 1.5 cubic inches per day for convenience.
Similarly, we can approximate the unicorn horn using a cone of the same base diameter, and we get 19.34 cubic inches for a 3 foot horn. Even if the horn were as robust as the antler of a whitetail deer, the rest of the herd could cover for a unicorn that lost it's horn for the 12 days it would take to completely regrow it's horn, or the 8 days it would take to get to a usable 2 foot horn.
A delicate horn that's intended to break away should require even less material, and would have a correspondingly reduced regrowth period, so 8-12 days provides a generous upper bound.