I never understood why that's the case. Is it not to encourage unlawful activity?

Stealing an example from mr robot, if I break into someone's computer and find evidence that proves they are trafficking underage photos, I don't see why that proof should be ignored , in any circumstances.

Sure, charge me as well with breaking into someone's computer, if you can catch me, but don't dismiss my evidence.

Sure, and that's probably best. In my original comment, I specifically mentioned that what the FBI is asking for is reasonable providing there is a warrant, which would imply that they're gathering evidence lawfully.