Piping curl into the shell is bad because the server can choose to serve malicious content to your curl that it didn't show in the browser.

And to head off objections, Piping curl into the shell does not leave any record on disk, unlike the "download .... ./execute" workflow in which it is trivial and natural to insert "and take a quick peek at it too".

Edit: And in the best case scenario, where the script delivered by curl is perfectly innocent, it is still a bad idea since you are left with no authoritative record of what was done. You could run curl again in the future, but that assumes that the same version is delivered, or that the file is still there at all.