Species which we eat but don't farm we tend to eat to extinction. Think of the Atlantic cod fish.
Most oysters we eat are farmed. And you need the old shells as a substrate to grow a new oyster bed.
They are being reproduced (not a mistake here, they don't actually fuck/reproduce on their own) a lot that's true, but using the word 'successful' to describe their fate seems a bit too cynical.
Pretty much everyone eating well and having a good time.
Other human food species are extinct due to a combination of being a human food source and a food source for invasive species introduced by humans (eg, the Domed Rodrigues giant tortoise).
Famously the American buffalo went from 60 million in the late 1700s to 541 a century later. It was a cheap meat, provided cheap leather, and in order to deprive Plains Indians from a food source, the US government decided not to protect it earlier.
Then there's the collapse of many marine species due to overfishing, most recently the king and snow crab population collapse which canceled the season in Alaska, and the continuing question of the role humans played in the Quaternary extinction event.
Therefore, I suspect your claim isn't so clear-cut.
The US government actively supported exterminating it. That included having people shoot them dead from passing trains.
The most successful land animals today are... cows, pigs and chicken.
(Compare with horses, which were successful because they were useful... until they weren't anymore, and their population dropped. And yes, this also implies that lab-grown meat is an extinction-level threat for aforementioned farm animals.)