Well, it’s impossible to ban natural clouds but planes could avoid making contrails by just not flying in the zone where their exhaust would cause them. Source: I was a weatherman in the Air Force and would tell military pilots where to fly to not have a shiny line pointing to their exact location if such information could be a concern.
I never thought it about as a green house thing before though I do remember reading an article many years ago that contrails do contribute when they spread out into cirrostratus clouds.
I was a meteorologist in the Air Force and did make forecasts telling pilots at what levels to fly to avoid making contrails since having a long silver line pointing to your exact location makes sneak attacks a little difficult. Perhaps commercial airlines should make use of that information. It’s usually just a few thousand foot difference. Fly a little higher or lower and problem solved.
In answer to your question: yes. Humid cold pure air. By pure, I mean no contaminates until the hyrdrocarbons from the jet fuel are emitted into that pure, moist air. To form a droplet, a nucleus is needed. The hydrocarbons of the jet engine exhaust provide that nuclueus.