I am more or less aware of these scenarios and they certainly raise some concerns about potential for abuse, but the problem is that the opposite scenario where

I am more or less aware of these scenarios and they certainly raise some concerns about potential for abuse, but the problem is that the opposite scenario where federal agents or LEOs of any kind can not lie is not feasible. I asked another commenter below for an example of someone being convicted of making false statements when they did not know they were speaking to a federal agent, I would like to see one as the lying in the example above was during a formal interview process. I also find that a lot of these sorts of scenarios assume that the courts are incompetent, that the burden of proof does not still apply. The judiciary has a duty to apply the law in a reasonable way that complies with its intent - I doubt any judge would regard the intent of the false statements law to be to allow an FBI agent to tell someone to lie to them so they can then catch them lying and convict them. (This of course is why if you undermine the courts you undermine democracy.)