I have noticed this in a couple of scripting languages, but in this example, I am using python. In many tutorials, they would start with #!/usr/bin/python3 on the first line. I don't understand why we have this.

Shouldn't the operating system know it's a python script (obviously it's installed since you are making a reference to it)
What if the user is using a operating system that isn't unix based
The language is installed in a different folder for whatever reason
The user has a different version. Especially when it's not a full version number(Like Python3 vs Python32)

If anything, I could see this breaking the python script because of the listed reasons above.
Actually the determination of what type of file a file is very complicated, so now the operating system can't just know.  It can make lots of guesses based on -

extension
UTI
MIME

But the command line doesn't bother with all that, because it runs on a limited backwards compatible layer, from when that fancy nonsense didn't mean anything. If you double click it sure, a modern OS can figure that out- but if you run it from a terminal then no, because the terminal doesn't care about your fancy OS specific file typing APIs.
Regarding the other points. It's a convenience, it's similarly possible to run 
python3 path/to/your/script
If your python isn't in the path specified, then it won't work, but we tend to install things to make stuff like this work, not the other way around.  It doesn't actually matter if you're under *nix, it's up to your shell whether to consider this line because it's a shellcode.  So for example you can run bash under Windows.
You can actually ommit this line entirely, it just mean the caller will have to specify an interpreter.  Also don't put your interpreters in nonstandard locations and then try to call scripts without providing an interpreter.
Purpose of #!/usr/bin/python3 shebang