Most of those tube guys believe they are characteristically "warm," which works well with overly bright horns. But they have never seen a FR plot of a tube amp. The tubes themselves are capable of very high bandwidth. The output transformers typically serve as the terminal FR filter for the output stage. Couple that with any RC filters upstream, and you arrive at your final FR. Most designers of Hi-Fi tube amps minimize RC filters (and even DC decoupling stages where possible) and use high bandwidth output transformers with minimal negative feedback.
Example. The result is a flat FR from ~30Hz to >20KHz at steady state, constant load operation. So, not warm. At all. High frequency can and does roll off, depending on the reactive load seen by the output stage at any given time, but the roll-off is typically above 15KHz, where adults have diminished hearing. Compare that to the PIR graph, and you will see little impact in terms of "warmth". There are significant problems well below that F.
What they are hearing as "warmth" is progressive harmonic "soft clipping," "even order" distortion and related undertones / overtones.
From a high fidelity point of view, such amplification is flawed and outdated. It is fine to like the tactile feel, heat, pretty glowing glass, nostalgia, physical rituals, etc. of tube amplification (and turntables for that matter), but to believe tubes are the epitome of fidelity is magical thinking. I like tube amps, but I am intellectually honest about why.
Back to the Heresy IV... One of my best friends owns a pair. He has them in a small room positioned 1' from the front wall and 2' from the side walls. His electronics are SOTA: Matrix and Benchmark. (<-- Rut Roh!) I have spent quality time with them. I kind of like that they always have a live music-like presentation thanks to their horny PA speaker-like character and resonances. They are definitely "forward" sounding. They definitely also have a notchy response. I didn't notice them as being terribly bass shy, except in the sub bass frequencies, but he does have them positioned for maximum room mode exploitation. I could have a pair as a second pair of "fun" speakers, but could not live with them as a "reference" pair.
But I don't begrudge anyone else for liking or even loving them. Different strokes for different folks and all that.