What really puzzles me is the tendency of some cooks to boil or stew garlic for extended periods of time. Even if you don't dice it finely, as I usually do, some of it is going to be destroyed in terms of flavor, and you won't get as much "bang for the buck". You can add less garlic, avoid cooking it for long and get the same result! Can't you? Could it really make sense to cook garlic for more than one minute? I got that figure from one Georgian chef (Georgia meaning "a country in Eastern Europe")
It's not about "bang for the buck" - it's about different flavor profiles from the same ingredient. A small amount of nearly-raw garlic is not the same as a large amount of cooked garlic, which appears to be the false equivalence you've drawn.
As a very simple example that's highly illustrative, take a head of garlic and follow a recipe for "roasted garlic."
Depends on the cuisine, and the recipe. Cooking garlic for a long time generally makes it milder.
In some traditions, garlic can be cooked whole for a long time. In French cuisine for example, such as when making garlic confit, in which whole garlic cloves are cooked in oil for around 30 minutes or more to make them mild and creamy.
In Italian cuisine, many sauces begin by cooking whole garlic cloves in olive oil slowly for a few minutes to infuse the oil with garlic flavour, then the garlic is removed.
In Indian cuisine garlic, ginger and other raw spices are often cooked for a while, say 10 minutes or more when preparing a masala paste, prior to using it to make a curry sauce.
How you cook garlic has substantial affects on it's flavor.
I use garlic in four different ways, each providing different flavors:
Raw, grated. (Good for Guacamole). Very intense, so, use it small amounts.
Diced and pan-toasted. I tend to overcook mine out of laziness, because I want to caramelize the onions, and I just toss in the garlic at the same time.
Oven-roasted and frozen in vacuum-sealed bags. This makes them almost a paste you can squeeze out onto bread or toss into anything else you're cooking.
Finally, I pressure-can whole garlic cloves, providing self-stable jars. This process caramelizes the garlic in a fantastically delicious way, and are fantastic on sandwiches, salads, or on bread. They are so delicious, nearly everyone in my family, myself included, enjoys eating entire garlic cloves straight out of the jar. It's practically candy.
In Japan, they also do something where they bury garlic in the ashes of a fire for an extended time, "burning" it to almost complete blackness, and swear it is fantastic. I've never tried it personally, and don't know the preparation details.
Each of these cook them for different durations in different ways, and provide pretty substantially different tastes.