I think all experiments are began with some premonition of what to expect. For example Michaelson and Morley very much expected to measure the speed through which earth would pass through aether ... except they couldn't. An the results pushed physics toward theory of relativity.
I disagree that's it's an entirely bad process to bankroll experiments based on unproven promises. This is exactly how the Manhattan Project happened. The physicists promised that it was very likely they could create a very large explosion, but they did not know if it would bang or fizzle. So, the US government began a huge industrial scale operation to enrich uranium and to assemble the bomb. The first atomic bomb explosion was very much empirical science that was bankrolled by "unsound" promises.
In this sense going beyond LHC would be kinda ground breaking - big budget science with absolutely no clue on what to expect. It's how discoveries are made, yes, but I'm not sure if any large scale scientific project has been funded without at least some clue on what to expect.