Your idea is already addressed by standard criminal procedure, except for the bizarre part about letting the defense strike off any charge of its choosing.

In a nutshell: after the arraignment but before trial, they have a court hearing (the "preliminary hearing" aka "probable cause hearing", see http://en.wikipedia.org/wiki/Preliminary_hearing for a layman's description) in which the prosecution is required to lay out sufficient evidence to justify each charge. They don't have to provide evidence sufficient to prove guilt (yet, because that is the jury's function) but they have to show sufficient evidence that a jury could find guilt. Charges which do not satisfy even this basic level of substantiation are dropped by the court.

Edit: You can downvote this comment all you want; it doesn't change the fact that preliminary hearings have been a basic part of US criminal jurisprudence for decades, functioning more or less exactly as described above.