I get my stock from one specific LFS. I'm hesitant to blame them, as their tanks are immaculate, they have an outstanding reputation, and staff seems knowledgeable.
Never a good idea to assume a store is doing something unless you see it yourself. Especially if you're losing up to 50% of fish you buy. Most (there are exceptions) aren't quarantining, aren't making an effort to monitor for potential illness, aren't always treating for minor illnesses when they see them, take few preventive measures. Sales volume means survival for a business like that and they have to move stock quickly.
They may have nice-looking tanks, have otherwise good practices and be well-meaning. But business is business and corners get cut with the best of local shops. Just the nature of the beast.
What is the function of a quarantine for new fish? I understand it decreases stress, but the only difference between a quarantine tank and the regular tank is no hardscape, plants, or other species. How does quarantine help increase survival rates of newly added fish?
Health. The same reason you'd quarantine yourself to prevent potential shedding of a virus you don't know you have and unintentionally infecting another person. The function of a quarantine for any animal you get: ensure health. If you're losing 50% of fish in less than a month? You probably could have treated for illnesses (preventive or active) and figured things out relatively quickly in a quarantine setup. Ignore stress for the most part when it comes to quarantine. It's relatively easy to make livestock feel comfortable and that will vary among species. But once fish calm down, their immune systems adjust, they adapt to new food (you get to closely monitor digestion and waste), new conditions and many illnesses can become apparent that may otherwise be tough to spot among plants and hardscape.
A quarantine tank ideally makes it easier to
closely observe livestock to monitor for behavior and illness. That's not easy to do in an aquascaped system for myriad reasons, some of which I mentioned above. Not something to gloss over - especially if you plan to put them in an established system. Being able to
quickly treat with meds alone increases the likelihood of survival. Knowing how a fish eats and poops - something that isn't always apparent with substrate, hardscape, etc - is a bigger deal than most would think. Particularly when it comes to parasites among farmed fish, as some can survive outside the fish and even thrive in a tank. Particularly when it comes to getting wild-caught fish to adjust to dry or frozen food - especially tiny hunters like Boraras or similar. Monitoring closely for injury without the obstacle of hardscape, substrate, plants and such is beyond helpful.
Many diseases are difficult to treat in a well-established, scaped tank because you may have to tear them down in order to successfully eradicate whatever the problem happens be. In a quarantine system? Dump it, clean it, reuse it when necessary. Less risk of ruining things for other livestock down the road (like invertebrates), as well. Gotta treat with copper in quarantine? Fine. Won't end up nuking any shrimp you add a year down the road or if you reuse the tank or components later on. Gotta de-worm? No risk of killing off your snails.
Many illnesses don't become apparent for 4-6 weeks and just dumping fish into your display tank without taking preventive measures (especially after losing so many, as you unfortunately have) is just begging for trouble. A quarantine setup doesn't have to be permanent or even an aquarium. Can be as simple as a Rubbermaid tote or bucket that allows easy access. Ideally you'll use an aquarium of some sort or something that's clear, though. I keep spare sponge filters running on my main tanks so I always have a sponge I can use for a quarantine. Just clean it when done and pop it into storage until I need to replace a sponge I'm using for quarantine. The tank I use the most for quarantining goes on a shelf when not in use and I use it to store tank extras - filter media, food, tools, fertilizer, meds, fake plants for QT, that kind of stuff.
As someone who reads hundreds of thousands of posts per year and tens of thousands from newcomers to the hobby? There's one thing that is abundantly clear when illness is involved: most haven't quarantined anything and they have a mess on their hands that could have been easily prevented. Even among longterm hobbyists. Pretty much every "OMG what's wrong with my fish?!" post goes the same way.