Hmmmm sounds like the government can launch endless bs investigations, wait for their target to throw something (anything, a piece of paper, whatever) in the trash then charge them with destruction of evidence. A infinite guilty-change glitch if you will.

That's what judges are for, so cute hacks like "putting everyone in the US under "investigation" won't work. That said, if I was under investigation, you bet your ass I'd be extra diligent in ensuring I'm not accidentally shredding any documents.

What you're describing is malicious prosecution or abuse of process. It's illegal and it would destroy the prosecution's case. Not only that, but the victim could sue for damages.