To be clear this would not prevent every instance of lying, but the current state is in most cases manifest shameless lying or deceits that surface some years later, so it would be a stratospheric improvement, in my opinion.
By whom are laws enforced, and by whom are those people appointed and to whom do they answer?
Or, to take another angle, why don't the prohibitions in FISA effectively stop the government from abusing foreign intelligence apparatus for domestic spying?
Of course the judicial, legislative and executive branches should be independent and they're not that much right now.
In any case, even in such a system the proposal might have more positive than negative effects, and maybe lead to gradual improvements to everything else.
Or it might make things even worse. After all,the FISA court system itself was created in response to abuses by the CIA and FBI (and others) as a way to check their power. Instead, it became a (secret and opaque) rubber stamp that approves over 99% of all warrant applications.
Yes, you're just proposing making it a crime for politicians to lie without addressing who/what will determine that they're lying and how, and can't seem to see any possible problems or abuses of your proposed system.