The obvious one is enforcement would be a political football; see for example the Trump presidency "emoluments" scandal vs. the whinging about Pelosi's investment performance. It'd never end and the quality of the candidates or decisions they make would stay the same.
Another is that it'd be unfair to politicians who think that market indexes are a bad idea.
Has anyone made a credible argument for why top national leaders should be allowed to stock-pick?
(Rather than required to put any investments into total-market index funds, which is good enough for the little people.)