I can record a quiet song with no apparent preamp noise using a quality preamp's higher gain setting (EIN gets higher the higher gain you use); I can also record a louder song by dialling the gain down (EIN decreases, but this doesn't really matter because the signal is strong compared to the preamp's noise floor). What I can't do is use the low gain setting for BOTH sections of music (the only option we have when we don't know when they're coming), and expect the less-than-ideal staging for the quiet parts to sound good. Of course this is only really relevant if you're using compression or amplifying certain songs in post, but some bands really do get that loud AND that quiet, and it's a terrible experience to listen back without narrowing the dynamic range.
this is all simple to do in post, without any guessing. As you mentioned, you raise the noise floor when you raise the gain in the field. thats fixed to your mic self noise and room noise, all of which gets amplified whether you do it in real time or post.
That's the thing though, you are assuming the main source of noise is the mic self noise and room noise. But I can consistently hear the preamp self-noise before either of those, when we're talking about recorders like the Zoom H series, or the Roland R-05, or the Sony PCM-M10. The Zoom H1 and H1N, for example, automatically switch circuits when you increase your gain past +13dB or so - you can clearly hear a drop in hiss when you go from +12 dB to +13 dB, even though you're getting more gain. The same is true of the Roland's MicLOW and MicHI gain settings: their gain range overlaps, so if you set both to the same point in their overlapping range, MicHI will very clearly sound less noisy, and that becomes particularly apparent when you add even more gain digitally in post.
The thing about the Zoom F3 is that not only does it have cleaner pre-amps than the aforementioned recorders, but it also works in such a way that you don't have to pick between MicLOW and MicHI, it will just switch automatically as needed. Maybe our use cases are too different, I don't know. What I'm saying is particularly true when you're using mics that aren't too sensitive and you aren't using any external pre-amps, so you're always using Mic instead of Line In (I appreciate your point that if your signal is hot enough, the F3 just applies a pad, but my mics without an external pre-amp are basically never hot enough).
I agree this discussion is not particularly relevant to the Deity PR-2, except for the fact that supposedly its pre-preamp outperforms all the recorders I've mentioned except the Zoom F3 and the MixPre. At this point the advantage of the Deity over the worse recorders I've mentioned is the size, battery life, 5V PiP and MAYBE pre-amp quality, but that's it.
