Keeping hot snakes in your home is definitely not a good idea. You will get bitten eventually, and you'd better keep your own supply of antivenin since there's not much cobra antivenin in the US.

On the plus side, an escaped cobra probably won't live long in the wilds of Wisconsin. No other cobras to mate with, different food supply, and it's too cold.

Keeping antivenom on hand isn't that common for keepers. Antivenom production is limited, so is its shelf life, it makes more sense to keep it at centralized locations. In any case, doctors prefer not to give antivenom, because it can be worse than the bite itself.

Even tropical snakes can stay alive in a home, or a settlement. I wouldn't expect them to breed, except of course in Florida where apparently all kinds of reptiles can become pests.

I would expect it to be uncommon for keepers of pit vipers and corals in the US to stock antivenom, but I'd expect it to be common for keepers of non-native snakes because US hospitals don't stock non-native antivenoms. You'd typically have to obtain it from a zoo that keeps exotic snakes.

Antivenom is never "worse than the bite itself." It can occasionally cause an anaphylactic reaction which is easily manageable in a hospital setting by administration of epinephrine. The reasons doctors hold back on antivenom is that a significant fraction of people come in to the ER thinking they've been bitten by a venomous snake when they haven't, or they've received a dry bite from a venomous snake. Antivenom is never administered until venom symptoms are evident because it's quite expensive and there's no reason to risk a (manageable) anaphylactic reaction if it's not necessary.

Withholding snake* antivenom once symptoms are evident would often be a death sentence, and always medical malpractice.

https://www.sciencedirect.com/topics/neuroscience/antivenom

*Edit: Added the word "snake" because black widow antivenom exists but BW bites are not usually life-threatening in adults. Most people can pull through without it. This is much more risky with venomous snakes.

A zoo would be a centralized source. Depending on the country, there are central hotlines to help doctors know what they need and where they can get it.

An anaphylactic reaction on top of a snake bite can be worse than just a snake bite, but of course it depends on the circumstances and species. Also the immune reactions from the antivenom may clot the kidneys, which are probably already a concern if the patient is in shock. And yes, all of this is manageable. Immunology can be really weird and complicated...