Agree with all of your points. Thankfully when it comes to genetic diversity in dog's the Leonberger breeder community is working together on the details and process instead of just "Doodling." There is an Int'l database to track lines and prevent in-breeding. It's a fragile thing to maintain the traits of the breed and breed standard while trying to better the breed's inherent health issues. That's the dog world. The chicken world isn't alot different, just not at all managed this way.Other than appearance I don't think breed means much of anything. What traits the breeder selects for when deciding which chickens get to breed means a lot more. If they know what they are doing the breeder decides which flocks lay well, how they typically behave, and how healthy they are regardless of breed. Breeds can have tendencies but only if the breeder selects for those. For example, Buff Orps have a reputation of going broody. If the breeder selects for hens that do not go broody within a very few generations you can have a flock where a hen going broody is pretty rare. If a breeder selects leghorns for going broody within a few generations you can have a flock of leghorns that have a lot of broody hens. The same goes for any trait the breed is supposed to have. If the breeder selects for it or against it makes the difference in what you see in a flock.
Hybrid vigor is a real thing in animals. Plants too. Too much inbreeding can cause issues with health, productivity, fertility, and other things. Genetic diversity is important in flock maintenance. That does not mean you need to constantly bring in new genetics from a different breed. You can typically keep replacement girls and boys from your flock for a few generations before inbreeding causes a problem. You can regain genetic diversity by bringing in a rooster of the same breed that has been genetically isolated for several generations from your flock. Spiral breeding is how many breeders maintain genetic diversity without bringing in new chickens.
The principle of hybrid vigor is real. There are different techniques to manage it.