I don't think PCB assembly would be that cheap, especially for a board with lots of SMT components. What I understand is that SMT manufacturing has a high startup cost, you need to supply the factory with full tapes of parts, and the factory needs to program the assembly line, often a factory is reluctant to take any offer below tens thousand boards because its high overhead. Even for service providers specialized in prototyping then, I don't see many provide QFN and BGA packages as options.
What have I missed here?