I've done some (actually a pretty good amount of) DSP programming and have a few things to say on this topic - I think there's some confusion (and I may well add to it, but I at least have some comments about things I know, and questions about things I doubt that I've read in this thread...so here goes)
I see the main benefits of a 24 bit word length as: A) you can track with peaks safely below 0dBFS and still have ample dynamic range, and B) during processing, the higher word length means fewer rounding errors with all the math operations.
I think this is correct. Even further - there is no 24-bit data type in C, hence DAWs having a "32 bit audio engine" or "64 bit audio engine". Whatever your source is is upsampled into 32 bit floats or 64 bit doubles from the get-go.
One of the other advantages to using 24 bits instead of 16 is, when processing, any rounding errors will end up in the bottom bits. Those bottom bits get shaved off and all of those 'problems' go with it.
I think this is basically correct, too. The 16 most significant bits (or rather... the only 16 remaining bits), when downsampled from whatever the internal rate in your DAW is, is what you get "out", but with extra headroom the rounding errors don't really matter when truncated at the end (they're truncated out of the down-cast).
The reason for recording at 24 bit is that it provides a lower noise floor so you can record at a lower level and not ever have to worry about clipping. Recordings done at 16 bit have exactly as much resolution as those done at 24 bit but with a higher noise floor.
I think the lower noise floor is a side effect - I don't think the extra 8 bits are just used for noise floor purposes - the whole thing is actually recorded at a higher resolution and more accurately reflects the voltages on the convertors (whether or not the convertors have the technical capability to distinguish that many different voltages.....I'm not really sure - and I kinda doubt it).
The only time I'd bother recording at 24 bits is for a live event where there's a potential for unexpected loud volumes.
Are you sure that the extra 8 bits are used for "extra loud signals" only? I think this is an inaccurate statement for the same reason I think Boulder's was - just at the other end of the spectrum (and with the same caveat that I kinda doubt it even matters.... I just don't think you're right about what the extra bits are used for).
...I now work at 32 bit floating point. This is not to sound better, just to give more flexibility in the mix--I can do processes that raise the levels into what might be clipping at 16 bit then just normalise downwards.
I'm not sure it exactly relates to how DAW's work, but this is exactly the reason I always upsample to floats or doubles (64 bit floats) when doing any DSP programming - so there's not a clamp to 16-bit values at every stage - you only have to do that once at the end of the chain. Of course... the DSP programming I've done always uses 16 bit source material, so I think there may be a difference when taking into account higher resolution sources....but your point stands, and I agree with it - except that I would say it *does* sound better, to not downsample to 16 bits, repeatedly, every step of the way. Audibly, literally, better - but I think most DAWs use 32 or 64 bit internal processing anyway, which is basically the same....in which case - I still don't know if the source depth *really* mattered beyond 16 bits. I suppose some math examples might help.... if you start with x[n] and do y,z,a,b to the n samples in x, do you end up with a more accurate sample if x was sampled at 16 bits or 24? Almost certainly 24...but I don't know if it *really* matters, to be honest, since it's upsampled to 32 or 64 from the beginning, regardless, and we can't really distinguish more than is expressible in 16 bits.