If you think a tube is bad, replace it with the same type and reset the bias if you're able. Tube rolling won't make you a composer. Or a musician. Or even a producer. It will make you kind of cranky.
I agree you've made some good points. But your points I think generally derive from the assumption of desiring neutrality/accuracy, hence "the job of an amp and other components is not to alter the signal."
But as we know plenty of audiophiles don't approach the hobby like that. They aren't looking at their sound system as some neutral conduit, but as having a sonic presentation in of itself, and they want the system to "sound how they like." And also that the sound of a system can be nudged in the direction they want. This naturally invites the idea of personalizing your sound, of you having your own level of creative input to achieve a distinct result. A lot of people find this type of interaction gratifying. It's why, for instance, people may build their own speakers or amps, even though they could just buy off the shelf gear. Nature of the hobbyist.
And obviously tube rolling fits in to this idea perfectly - insofar as you buy in to the idea different tubes can change the sound, the hobbyist gets to play around and have fun. It's clear to me that many tube amp owners enjoy doing this.
Personally, even though I've owned different tube amps, and my current tube amps for 20 years or so, I was never in to tube rolling. Just couldn't be bothered. When I had to replace my power tubes, I'd just replace them with the same type of tube. Done. Never noticed a difference in the sound.
Last year, though, my amps started distorting. I traced the problem to the small input tubes. I realized I don't think I'd changed them since I bought the amp! Never needed to. To remedy the issue I grabbed some of the same type of tubes, though a different brand/era. Distortion was gone. But...the amps didn't sound the same! They sounded "ultra tubey" - lush to the point of mushy. None of the high frequency sparkle, none of the snap and punch to drums, bass a bit mushy. It sounded, for lack of better description, like an underpowered amp! I was totally bummed that I didn't have the sound I was used to.
So instead I looked at the original driver tubes I'd taken out, which were now out of production, and tracked down those exact same GE tubes (NOS).
Fingers crossed I replaced the new tubes with the those GE tubes and..voila! The whole sound snapped right back to how it had always been. Vivid, punchy as hell, etc. Total relief!
So your point is well taken that you can really just screw up the sound by random tube replacements.
But on the other hand...since then I actually ended up trying other different tubes in my amps - e.g. KT120 tubes in place of the usual 6550s - and have been pretty blown away at the results. Playing with different power and input tubes has been a blast, as I seem to have pushed the sound around in ways I really enjoy. Some combos seem to produce really tight, punchy sound with a tighter smaller soundstage/imaging, other combos seem to produce bigger, more lush sound, some combos tighter bass, some looser, etc.
I have no objective data to supply, so it's up to the reader how plausible he finds the idea of changing tubes might alter the sound of an amp, so ignore all that as you please. But if one accepts for sake of argument that tube rolling can alter the sound at all, and then ask "why would anyone bother playing with that?"...I can understand why.