The problem is mathematically it just doesn’t work. Humans are too good at reproducing. We’d be back in force before too long.

No, the only way is more death note style, taking out billionaires and some of their bootlicking buddies, and those who put profit over the planet’s health. It’s perfectly possible for the rest of us to patch things up—we almost did it with the ozone. (Until guess who decided they wanted to throw money around to force us to stop.)

If the half of the population includes the part that owns cars perhaps, but the carbon footprint of a person varries greatly. In general the more money someone has the higher the burden they are on the climate.

Idk, I feel like targeting living beings is different than targeting structures, even though I know a sudden lack of refined oil would lead to death. I'm just convinced they'll never stop until their own heat deaths.

No. People would starve to death. Cars are necessary. Not everyone lives in the CBD of the capital city.

Do they just dump it in a big hole and profit?

If your only problem is that you want more resources available for yourself, I can see how you'd come to that conclusion, but you're wrong. It wouldn't solve the underlying problems, and in fact it would create a whole set of new ones. Modern civilization depends heavily on economies of scale, and your magic finger snap does nothing to change how resources are produced, distributed, or consumed.

You're also assuming that every human consumes resources at roughly the same rate. They don't. Not even close. A tiny fraction of humanity consumes vastly more resources than billions of other people. Your finger snap doesn't address that inequality at all. The same people and systems that concentrate resources now would simply have an even larger pool of resources to hoover up afterward. Then what? Snap your fingers again?

And follow the logic to its conclusion. If reducing humanity to 100 million "solves" problems because fewer people are consuming resources and competing for them, then 1 million should be even better. Five thousand better still. Ultimately, zero humans means zero poverty, zero war, zero homelessness, zero human carbon emissions, and zero human suffering. Problem solved!

Except obviously it isn't, because eliminating the people who experience a problem is not the same thing as solving the problem for those people.

We don't have billions of people living in poverty because there simply isn't enough stuff on Earth to go around. We have enormous disparities in who controls resources and who gets to consume them. Fantasizing about eliminating most of humanity while leaving that system completely intact makes you a stooge for the oligarchs.