This is actually something that's kinda bugged me for a while now. There's no question that it uses more battery. Being a technical person, I even totally understand the "why". To me the real question is, how much battery loss are we talking about? If I'm losing 1% during my day from this habit, I'm fine with that. If I'm losing 50% of my battery per day, that's a big deal. So while I have absolutely no doubt that I'm losing battery from closing things I shouldn't be closing, I'm just not convinced that it's enough to be concerned about. I know I've never noticed a measurable difference and I've been closing things since we could close things (and have tested NOT closing things as well).
Just because it's a true fact doesn't means that it's worth worrying about. But I'm ready to be convinced otherwise.