The polite form is also a way of distancing yourself from another person. I read somewhere that you would use तू when addressing your creator, and I'm not talking about your mom and dad here. So perhaps आप is fine when you're smiting the anti-christ (or whatever).
So this was causing me a lot of confusion because of the हैं instead of हो. So I talked about it with my parents, and we agreed that it should be हैं when आप refers to more than one person and हो when आप only refers to a single person. We are from New Delhi for reference.
Are you guys Punjabi? There is no "आप" officially in Punjabi, and हो (which goes with /tusīṅ/, "you") is the most polite form. But, under the influence of Hindi (I assume), Punjabi speakers sometimes try to squeeze aap into there and make it work. हैं is not a plural in standard Punjabi, but it can be there in dialects. So I'd guess people adapt aap to replace /tusīṅ...ho/ as an "extra polite" form of "you", and use हैं when it's "you-all". What do you think?