John Atwood (One Electron, Artemis Labs, etc.) has a fairly concise commentary on some of the design considerations you mention (post #2 of this thread in DIYaudio: http://www.diyaudio.com/forums/tubes-valves/132233-fixed-vs-cathode-bias.html).
I'm thinking that the hot running cathode-biased amps you've experienced were more of a design choice for maximum power than anything else.
There are certainly different issues at play with a cathode biased amp from that of fixed bias. For example, the quality of the cathode resistor's bypass capacitor can have a noticeable effect on the amplifier's sound. Typically (due to the required value), they're electrolytics, although bypassing them with a high quality cap can work.
I'm not arguing in favor of one technique over another, but one serendipitous attribute of cathode bias is that you might loose fewer (or no) parts if a tube shorts out (a plate or screen to cathode short).
Of course you can build protection into a fixed bias amp to address this. I think the Prima Lunas do this. It's a nice feature.
I think that sonic considerations for fixed/auto bias are more evident in guitar amps where the output stage is pushed very hard. At this point, the time constant in a cathode biased amplifier (the recovery time) John refers to in his post comes into play, and cathode biased guitar amps have a slightly softer edge to them as a result.
My thinking about audio in general, is that as design architectures "mature" (move higher up the sonic food chain), their sound converges ... toward reality.
And so it goes ...
Cheers,
Thom @ Galibier Design