There's audio processing stuff that I'd love to do in web browsers, but I refuse to touch Javascript with a ten-foot pole. I am the kind of person that would like NaCl to be adopted outside of Chrome. If you are the kind of person that is more interested in building the "app" part of some application of that kind of program, you have nothing to fear from NaCl -- just think of it as opening up the "standard native code" (native browser code, like video codecs, gzip decompression, etc) part of the web browser to everyone. You don't really care about what's going on under the hood when your users decompress some data you served to them, as long as everything works properly, right? That's pretty much the definition of something that most web developers couldn't care less about, and that people who do (for lack of a better term) "fast computing" care desperately about.
To give a recent example, what if you'd like to start serving Opus audio to all your users? The standard response to that idea now is "that's funny, Internet Explorer will never even support Vorbis, and that's over a decade old." If safe native code execution was a standard part of the browser right now, it would be trivial to distribute an Opus decoder alongside the "web app" you implemented in Javascript. Opus would just be your competitive advantage, not something you need to beg people to implement. It would already be ubiquitous.
Before anyone mentions X implementation of Y audio codec in Javascript in an attempt to discredit the value of native code execution, just stop. I highly doubt it will work acceptably on my mom's computer (the average computer that accesses your site is almost surely a hell of a lot less powerful than you may assume it is), and I highly doubt you'll ever be able to rival the performance of native code for processing on the order of video codecs anyways. Not to mention the fact that the majority of the nontrivial Javascript audio demos you've heard were made possible in no small part due to standardized, native code linear filtering and convolution.
"Frustration" would be the word that sums up the whole "web app" movement to me. When I see that someone's made a client-side GIF animating "web app," all I can think about is how it would have taken two seconds to hook an existing highly performant C GIF encoder up to some Javascript, and instead we had to wait for someone who knows Javascript to hack a painfully slow (and therefore useless for the vast majority of users) alternative together. You know how ubiquitous similar server-side services are? That's because all it takes to make one is a simple Javascript/HTML form (or HTTP, if you want to get trivial)-based interface to an existing C program. Just think of where client side web apps could be right now if the same were true for them.