As another HN reader who does security for a living, perhaps I can add some specific points. (I know this thread is probably dead given that it is 1 day old, but I access this site via HN Daily now so bear with me.)
* No transport security. As many people mention, at least adding HTTPS would help with this. However, most non-browser SSL clients (wget, curl) don't include any root certs by default so even switching to SSL would not help this method. Firesheep, sslstrip, etc. automatically generate a self-signed cert which would look no different to wget than a real cert.
* No persistence. If you download any installer package once and then reuse it on multiple machines, you get the benefit of knowing that the same code was installed on each machine (good or bad). With this method, users may catch the site in the middle of an update and get multiple versions of the package.
* No authentication. Even with SSL, you only get strong transport security. You would know strongly that ".pow.cx" sent you some code, but not how that code got put on the server. With package-signing, typically done on the developer's end system, you know that it was protected even before it was uploaded to some site.
* Easier to trojan than binaries. Inserting a few extra shell commands in a single HTTP(S) session (say, targeting a single client IP) is much easier than building a custom binary package. Consider how hard it is to even compile Firefox with all the dependencies. Now do that work and insert a trojan and upload a separate 10 MB binary that needs to be stored somewhere on the server while waiting for that one client to visit the site. Compare this to keeping a two-line patch to a shell script (easily done in RAM, maybe even by hotpatch).
* Trains users that all the above is ok since the popularity of this "| sh" install method is relatively new. (Yes, I know about shar scripts in the past but those ended by 1996 or so with the advent of real package managers). It is absolutely impossible to retrofit "| sh" to be secure, whereas it is definitely feasible to add package signature verification support to gem or yum or apt or whatever (in fact, all those already support it).
The fact that many installers aren't signed today is not an ok to drive this process back to the 80's. We should be moving toward the future when package signing is a required part of being a software developer. Too hard? Well build tools to make this easier!