I'm not sure I understand what you mean about the air mattress on the sofa bed. Is that something you have to blow up each time before use or can you close the sofa with the bed inflated?
I also think latex mattresses were the standard years ago but for some reason they fell out of favor - not sure why.
That air mattress over coils... it's an 'Air Dream' if you want to google it. I bought it over the internet when I got sick and tired of the crappy sofa mattresses that you get with a pull-out (even the upgraded sofa mattresses stink). It has coils like a regular pull out mattress but it has an inflatable part on top and it's all contained in a regular type mattress cover, very sturdy and you wouldnt know it was an air mattress by looking at it. It comes with a plug in pump and it takes maybe 30 or so seconds to fill it. Same when you let the air out. It isn't a pain or anything to do and it folds up nicely back into the sofa. I've had a ton of compliments from overnight guests and due to an odd work schedule for me (before I got laid off :-) ), I've slept on it myself when I dont want to wake my husband and I love it.
I was leary about it since I bought it sight unseen but it was a very good purchase. I think I remember seeing a small clip of it on the internet - showing what it looks like and how it is inflated. I think people mostly use it for their camper or boat mattresses when they dont want to sleep on a regular pull out mattress for comfort reasons. Anyway, I shouldnt curse myself, but this air dream mattress gets used quite a bit due to many teenaged nieces and nephews sleeping over :-)