Emacs is free software and people typically download a binary to use it. Is that dangerous somehow? The source code is in a well known location.
I agree that it is troubling that nonfree JavaScript is shipped all the time, but again, that happens every day without asm.js being involved, and asm.js does not help or hinder this.
The main reason free software saw such adoption was that it was very high quality software available for free. Most people aren't even aware of the philosophy and history behind it, nor would they base their decision on what software to use on that philosophy and history.
Web services aren't covered by free software licenses, but they generally have no cost, are sandboxed, and you don't have to install them (even though you're actually "installing" them a lot, just in the background). For almost all users, that's a huge win, but for free software, that's a huge loss.
asm.js enabled many more classes of software to run in this environment, and I think that's a big looming negative for software freedom. I love Mozilla and I think what they do is amazing on almost every level. But the web is more than just a browser and JavaScript. There's 65k ports and dozens (hundreds?) of protocols. There's no need for the battle for the open web to take place only in the browser space.
I do think you've hit on something though:
> People ship nonfree, minified JavaScript all the time
I know, and I think it's dangerous for software freedom if the apps we start depending on are all closed-source web services, where we're at the mercy of the owners. Vendor lock-in is vendor lock-in, no matter the distribution channel, and zero-install isn't worth it.