It wouldn't be cheaper. It would be substantially more expensive because the research was undirected. Spinoffs come from solving one problem and finding a use for the technology elsewhere. If you don't solve the original problem you don't develop the technology to spin off. It's not the only way to do things but undirected research is difficult to fund and justify. Engineers don't go around solving problems at random as a general proposition. Students rarely solve serious engineering problems at all.
The proposed alternative to directed engineering for space flight is directed engineering for other stuff, not random engineering. I think space exploration is neat, but I reject the argument that it's uniquely justified because it's hard and creates spin-offs.
Curing cancers is hard. Building fusion reactors is hard. Detecting gravity waves is hard. If those things are more important (and they arguably are), then do those things and hope they accidentally apply to the space program.
What idiot would argue that the trying to cure cancer would be more likely to advance rocket design than trying to design better rockets? Why is the inverse considered a serious argument? It's just propaganda for people who don't think space exploration is neat.