Butter is only a favorite because Lard has been some demonized that no chef would ever use it anymore.
Approximately nobody has access to high quality leaf lard like the food blogs champion.
Nope. Butter is favoured because it tastes unctuous. Nothing to do with Big Cow or any special interest lobby local to certain valleys in the USA. Except maybe Big Bacon Drippings, because if there's one thing better for a grill cheese than butter it's bacon grease (thick-sliced sourdough bread, sharp Cheddar cheese, a shmear of chili crisp)
Now, suet has been demonized to the point that nobody makes suet pudding any more. A shame, really.
Oily stuff tastes unctuous.
Butter is favored because most people had it in their youth. Some regions loves Nato and Chicken feet, others cheese and oysters. What's the most delicious? It depends of your own history.
I spread olive oil on my toast and prefer the croissants made with that as well. My favorite dish is fried tempeh.
You might be able to achieve something if you can somehow freeze your olive oil and chill your dough, and work very quickly during lamination, but you should, even with a lot of work and tweaking, still expect to get a noticeably inferior product for something like croissants.
Depending on how picky you are/not, you might still be personally happy with the texture and taste, but don't expect to get even remotely close to an actual good butter croissant, by more objective standards. Here in Canada we had a minor problem with the butter texture due to what we feed our cows here ("buttergate"), and this was preventing professional bakers from achieving quality croissants with just the Canadian butter. This should make you highly skeptical that you can get anything good with something as different as olive oil.
Still, I do love the idea of an olive oil croissant, it would be delicious.
I am thinking if an ideal butter croissant has some flaky fluffiness (perhaps if we define it as "trapped volume" between flakes), and we define this ideal flakiness to be 100%, then you can extremely easily get to 20% with just olive oil. Frankly I think you might even get close to 50% (defined in this way) provided you also start with a trustworthy recipe by mass and that aims for proper hydration (e.g. https://www.seriouseats.com/croissants-recipe-11863500) and work quickly with lots of chilling.
Just, subjectively, you might realize that 20-50%, defined this way, isn't much like a proper French croissant, and is more like a cheap doughy supermarket chain croissant—which I do still frankly enjoy sometimes anyway!
"Unctuous" is certainly not specific enough, the reason butter (and ghee) is so delicious is its butteriness, i.e. it has a highly distinct taste. All properly rendered animal fats have highly distinct tastes and serve different purposes. Schmaltz tastes slightly of chicken, duck fat of duck, lard of pork, and tallow of beef.
But butter does NOT distinctly taste of beef, rather, it is reminiscent of slightly-aged milk (or, in the case of ghee, it may even strongly smell like certain kinds of aged cheese). There is, also, in butter, significant absorbed water content, and, to my palate, even a very subtle acidity that is not quite present in other rendered animal fats that give it a sort of brightness that make it work in things like butter-creams and other delicate or mild flavours (e.g. popcorn).
It is IMO this specifically "non-meaty" unctuousness that is the real draw of butter. Not some childhood nostalgia.
Though my grandpa used lard on his bread in the great depression because they couldn't afford butter.