Well, no, nobody signed up for this program in full knowledge of the costs.
Here's this from Bloomberg:
Stephen Lovegrove.... the permanent secretary of the Ministry of Defence, said he’d be discussing the “slightly unknown territory” of long-term costs in meetings with F-35 program officials....“I am constantly being asked by parliamentarians in the U.K. what the total cost is going to be and they are sometimes, understandably, a bit frustrated when I have to tell them, ‘At the moment nobody is entirely sure,’” Lovegrove said.
Did the UK have knowledge of this when they joined the program? Did anyone (including Korea)?