That's the problem though, isn't it? Most activists and protesters _don't_ want to commit crime, they want to call attention to injustice and work to get it fixed. Undercover agents like this are given the job of turning peaceful people into "criminals" so that they can be arrested.
And while I'm sure "hur hur, let's actually go blow things up and loot shops" works sometimes, it's not going to convince you or most other people to turn to the dark side. The reason for the song is to remind you that it's usually _not_ so obvious. Maybe you get into the fed's car because he's always volunteered to drive for the last six months and you assume you're going to stop by a place he knows to get donuts. Maybe you've been having conversations in that car for six months and a lot of them have been about whether vigilantism can be ethical. Today the car pulls into a gun shop instead of a donut shop, and now you're under arrest and they have a recording snippet of you saying "look, I understand the desire to do violence against bad people BUT". They don't play the "but" part when they take you to court.
How do you protect against that? You have a silly little mnemonic song to remind you that the guy who always brings up the _idea_ of criming, and who always volunteers to drive, is suspicious.
The other big problem is that even the most peaceful activities - even your very existence - can be defined as a crime. Giving water to a dehydrated person can be a crime. Saying "trans rights are human rights" or "genocide is bad" can be a crime. If the Black Panthers, who by all accounts were intelligent and well-organized and focused on obviously good things like giving free lunch to schoolchildren, could be redefined in the public eye as dangerous violent criminals who it was okay to shoot in their sleep, I think it's safe to say neither you nor I can be confident in our ability to "just not commit crimes".