At the risk of TB heresy, I'd like to suggest that this depends on the context. I suspect what most of us are going for is to put on a good show. That means showing the audience (where we're fortunate enough to have one) a coordinated team and knows that we're there to give them a good time. There's no question that a bandmember appearing distracted, off in their own world, pleasuring themselves, trying to remember the parts they didn't practice, nervous-ticking, or showing their girlfriend how well they practiced "Longview" on stage doesn't contribute to that.
On the other hand, a little noise here and there might actually be a legitimate part of a show. For example, in the right setting, spontaneously starting a pad as the band leader preps to go into the first (or next) song can make the show better, not worse, especially while it helps to fill some necessary gap or build a bridge between numbers - particularly where the members coordinate and work together.
Or, say, you're playing a rock show in spandex (cover band in a bar or an originals act in an arena, whatever), the band comes out together, and the guitarist looks at the crowd and plays a big power chord and sticks a pick arm in the air, looking the crowd dead on, while the other guys and gals are getting strapped in. Then the drummer plays one big fill, answering that chord, the bassist makes some noise underneath, and the singer prances on, suede tassels on his chaps waving in perfect sync with his silky perm, and shouts something rock'n'roll. The fact that you didn't talk that through or chart it out doesn't mean you're not telling that roomful of mullets to get ready to rock. And if it's right, you'll get that same feedback (also appropriate here) right back from them.
Even a little tuning or tone checking can be part and parcel of telling people "here comes the band." The symphony reference is apt. No one is telling them not to tune. It's part of the rhythm of the show.
Having absolute rules about these things, devoid of context, robs us of spontaneity and energy. And if there's an obvious tension to it (for example, what persists after the OCD guy has beaten the now-resentful noodler into submission) that sucks the energy out of a room. Or maybe you have a group that's done this Holiday Inn gig a million times to pay the rent, plays Hotel California note-for-note limp, and is obviously bored. No not-noodling is going to save that show.
If the show doesn't call for noodling, of course, don't do it. A high-production, choreographed gig is effective because everything is tighter than a mosquito's ass, including no noodling. And that shows the audience that you're pros and you're there to show them a good time - at that show. But that's not every show.
Instead, I suggest it's better to focus on being keyed into one another and the audience, identifying what you're there for, and doing - or not doing - what serves the context and the show and brings you closer to the audience. If everything you do serves your team and your purpose and communicates with the folks who came out to see you, that's going to come through.
p.s. a big +1 to the no reflexive giving away the hook of the next song between songs. Unless of course, it's intentional and serves the show.
