White leghorns aren't hybrids. They aren't the result of two breeds crossed together to create a mixed breed bird.
The leghorn breed originated in Italy. It comes in several colors. It's accepted by the APA and has a breed standard. Maybe hatcheries are selling hybrid birds under the name of leghorn, but as was said they also sell easter eggers under the name ameraucana, and that's also not true. And really anything you get from a hatchery is going to be a poor representation of its breed.
Or maybe they have their own lines or strains of leghorn and are, for some reason, calling those hybrids, but those aren't hybrids unless they crossed another breed in at some point. And if that happened, then those birds aren't actually leghorns. There's a hatchery here that's done that - and they sell the resulting hybrids under the name Ideal 236, because they're not leghorns.
As was said, if you have actual white leghorns and you cross them to another strain of white leghorns, you haven't made a mixed breed hybrid, you've only made a flock of leghorns with more genetic diversity than before.
Info on the breed:
https://livestockconservancy.org/index.php/heritage/internal/leghorn
As to the original question, none of the high production breeds or hybrids are really what I would consider sustainable, since broodiness has been bred out of them to increase egg production. You'd need to keep either a second breed that does go broody or an incubator to continue to propagate them on your farm. Short of that, you'd have to keep buying new birds to replace the old as they stop laying.
If I was shooting for sustainable on a homestead, I wouldn't be looking at any of these breeds. Rather, I would be looking at a breed that both lays decently and will hatch its own chicks.