What you describe is more accurately called the "prosperity Gospel", not evangelical Christianity. Mainstream evangelical Christianity doesn't believe anything like what you describe.
What I describe is what I've seen in many evangelical churches over decades and in three different countries, first hand. Evangelicals like to think their flavor is immune from all that ailes other branches of Christianity. Yet they too look down on the sick and the poor, sometimes more than older and more traditional strains of the religion.
Non-prosperity gospel churches don’t say it out loud, but the implications are easy to draw. Massive ideological and cultural structures aren’t logical proofs, there are many contradictions.