Earlier quoted context omitted.
I see your point, but you can just as easily run "sh script" although that does imply that you already know that it's a shell script (obviously you wouldn't just run something from the internet without checking it first).
The .sh extension told me it's a shell script of some kind. I don't check everything I download from the internet; I don't think anyone does. It depends on what it is, where I'm getting it from, where I'm running it, etc. There are certainly some things I will review carefully, but other things I give just a quick check to see it's not in complete shambles, and others I barely check at all. I typically run the latest…
I would tend to agree that scripts for downloading from the internet should have a '.sh' extension to make it clear that it's a script as opposed to a binary.