Well, to me, it just seems like common courtesy. And you don't have to swallow it, do you? You could put it in a tissue and discard it later.
I don't chew gum often, mostly at work after lunch to freshen the breath.
I've tried those little strips you place on your tongue and they dissolve but that's unsatisfying. For one thing, my mouth is too big for just one and for another, the gum can pick up small particles of food, or so I say.
You must be huge...those strips are small but most powerful (certainly for my mouth)