Only get a pyranees (or other lgd) if you are ready and really want to be the owner of a very BIG DOG.
Yes, it's a dog with a job, but it will still have all the needs and expenses of a pet dog, but often more because of it's size and coat.
Pyrenees require a lot of brushing and grooming (seasonally, but it's still a big job,) expect to have to deal with mud covered mats of fur if you miss brushings during the shedding season. They will definitey get mats behind their ears that will need trimmed. They still need to be trained to have their nails cut regularly, and they are notorious roamers if not fenced in well. You also have to consider the entire range of canine behavioral problems that can come with any dog.
It might dig, chew and destroy things, it might bark incessantly, or like my friend's pyr, it might eat livestock.
If it's not spayed or neutered, it may display sex based behavioral problems.
My friend's is a goat dog from a dam that was raised with goats, and it doesn't eat her goats, but it does occasionally eat her ducks. :shrug:
Personally, I'd also be afraid a rabbit protection dog could become very bored with caged charges.
I'm not saying it's impossible to have a rabbit protector, but I've been on livestock groups on other sites, and there are those who chant "get and lgd, get an lgd!!" for everything. (Many are small time breeders who wanna sell puppies.)
Someone's gotta be the person to point out that any "trend" that involves dogs doesn't always play out well for the dog.
Before you bring home a puppy, consider what your plan is for that puppy if it doesn't "work out" as an lgd. Will you sell it as a pet, when it probably won't be housebroke or have other house manners? Will you foist it off on someone else to train? What about in 8 years when the dog is too old to be useful, or if it develops hip dysplasia or another expensive ailment?
On the other hand, I also don't consider trapping a very useful method of predator control. One could try to trap and relocate or kill every predator in your county (they will keep coming back though.) In the end, it's basically leaving your livestock out as a buffet, and generally only reacting AFTER you take losses. I never could wrap my head around the usefulness of that.
For mine, I just build in ways that predators cannot enter. Hardware cloth where predators can reach in, double layers of wire if I have to. Build once well, and spare yourself years of fuss. The $1000 you would otherwise spend on the dog (plus veterinary care) can be spent on materials, and actually last much longer than the lifespan of the lgd if you build well.
Now, if you just really want a big dog and will love it and brush it and care for it even if it doesn't give a fluff about the rabbits, then by all means, get one.
I love my caucasian ovcharka, even tho she's never going to be a livestock guardian, she guards the family well.