Nothing bad could possibly happen. [1]
Install with
curl http://issh.it/yadummy | sh
It all comes downs to whether you trust the source.
At least with the "curl http://xxx | sh" method you can also examine the contents of the script before running it, and even opt to run it after downloading it and checking it locally.
With binary apps off of internet sites, which is what people install and use dozens of times a month, no such luck.
All you said are true for binary blobs as well. The page could be MITM, etc.
"curl xxx | sh" style deployment has all the same disadvantages of binary blogs, but has the added advantage that you can download and check the code before executing it.
In short, `curl https://www.example.org/foo.sh` and `curl https://www.example.org/foo.sh | sh` can do different things :(