The real question is how many of those random people could conclusively clear themselves with an alibi. If 20% of those people don't remember or can't conclusively prove where they were... You now have a ton of suspects that each are just as likely the criminal and obviously at most one of them could have committed the crime.

Yes if you can narrow it down to 100 people and then further confirm their identity with DNA or other real evidence that is potentially useful (and only potentially... It may waste your time). But for any sort of petty crime it seems like it will almost always do more harm than good.