Interesting question.
There are several cathode biased amps that do use NFB, including Tweed Deluxe, and various Champs, however many don't, eg most Matchless, and VOX amps.
I suspect there are a number of reasons.
1) One issue with cathode biased amps is that when they are driven into class B loading and/or grid conduction then there is a significant DC component in the signal, which will charge up the cathode bypass cap, and exacerbate blocking distortion. When an amp has negative feedback applied there a very large jump in gain when the amp clips, so I suspect that this effect combined with the cathode bypass cap charging, could cause some quite nasty distortion artefacts.
2) My guess is that the more widespread use of NFB coincided historically with the increased use of fixed bias. Thus early 50s Fender amps tended to be cathode biased and have no NFB, but by the 60s virtually all were fixed bias and used NFB.
3) EL84s are most commonly used cathode biased, and in VOX amps were run open loop, so I suspect many manufacturers use them in this configuration.
