Because "Uh..we'll send you a bill when we're done for...like...whatever it costs. I guess?" Isn't going to go over well when responding to a potential clients

Because "Uh..we'll send you a bill when we're done for...like...whatever it costs. I guess?" Isn't going to go over well when responding to a potential clients RFP. It's that or give them an estimate, unless you have a 3rd way? Also, how did you come to the conclusion that "project management doesn't work" is a historical fact? Also also, if your teams' estimates are a farce you might consider starting to track time spent on projects and build up a base of real world numbers you can use as guidelines for future estimates. It worked wonders for us.