Surprisingly, the following could be seen as one of those ever-popular hot takes. Thus threatening to make this something bordering on rather important. It's all comparative, I guess. To be clear, I am addressing some recurring bits of what I perceive to be misinformation regarding primary and secondary cigar bands, and the stickers found at the bottom of corn cob tobacco pipe bowls.
For a good time now, I've been noticing folks share their thoughts on how cigar bands help keep cigars from essentially unrolling. More recently, I've seen pipers mention they leave the stickers on their pipes to reinforce heels against heat. Heel heat in wrestling is also misunderstood. "I hate that guy, he stinks," is high praise to heap on a heel. You won't get your wish of never seeing that guy again--you'll probably be seeing a lot more of him, in fact. Now, 'go home' heat, that's for another time.
Regardless of that and in the interest of Quick-Take promised brevity, bands and stickers do not aid in the reinforcement of rolls or bottoms. They are marketing tools and they are varying degrees of nice to look at. As to the marketing aspect, is it any wonder that a brand owner would look for any excuse near plausible to have his bands left on as long as possible? If all that's keeping your smoke from unraveling is that it's essentially being held together with tape--you got problems, bub.
(Cigar foot bands and ribbons do serve a protective purpose.)
Similarly and even more absurdly, a small paper sticker over a hardwood plug or bare-naked cob bottom offers virtually nothing insofar as protection against blow-outs. I don't know what else to say to that. Do these things help at all? Sure. In the same way a mouthful of chewing gum would've gotten the Titanic safely home via plugging the leak.
So rip them off immediately, or at what point? Up to you. It's all about your cozy comfort; which is the very thing that pipes and stogies are all about in their totality.
::: very :::