There is absolutely a right to be able to pay to lie to the masses, free from state interference: this is protected speech.
Companies like Twitter have a similar right to decline to run such advertising.
Speech rules are precise and should be discussed with precision.
There are specific categories of lie in relation to which lying is actionable or criminal: defamation, false light torts, perjury, fraud.
But the government can't criminalize the political equivalent of puffery no matter what kind of "damage to institutions" may arise, perceived or actual.
That concern of mine was before you mentioned spreading tx fees over many blocks. However, I think it still differs from classical demurrage in the sense that it doesn't apply to coins that have left circulation entirely (e.g. lost private keys), so it would (like Bitcoin today) inevitably lead to monetary deflation rather than stable prices.
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