A big thing no one has really covered. Pasteur didn't "create" penicillin, he discovered it.

The fungus is a naturally occurring part of it's local biome much like tomatoes are from South America. You can grow tomatoes all over the world, but couldn't until people went to the new world and brought seeds back.

You don't just time travel to ancient mesopotamia, water some dirt, and expect a tomato plant to appear, nor do you build a hot-tub in Antarctica and throw a raw steak in and say "the water temps right and there's meat, surely a crocodile will soon appear!" You're just going to grow/propogate whatever is native. Likewise you don't just make a happy fungus setup and get penicillin, it naturally occurred in a particular part of the world, outside of that part of the world you're just growing native fungus.