I'm arguing that a law like you're proposing will inevitably be enforced unequally, be enforced against people who spoke unpopular truths that powerful people claimed were legally lies, and will be used by powerful interests to suppress their enemies. This isn't pessimism, this is a "this has happened anytime this or anything similar to it has been tried" and anyone with the most basic understanding of human nature could see that.
Do you have some example where "this or anything similar to it has been tried" ?
In countries with poor institutions anyhow, powerful people don't need this law to suppress their enemies, any existing law applicable to politicians can be used!
If I'm utterly naive with no understanding of human nature though we could just stop it here.
If there isn't enough evidence nothing happens (not even investigations).
And the person determining whether to prosecute, the standards of proof etc. are the same as those for any other crime to which politicians can be subjected.
The risks of people "taking control of the institutions" are just the same as with the other crimes applicable to politicians; again you seem to be arguing for general immunity for politicians more than against this specific proposal