A single celebrity attempting to manipulate the stocks they own via public perception is a fundamentally different thing than a bunch of politicians using their legal power to manipulate the stocks they own for their own personal gain.
I guess this can sort of flow two ways, though. A politician might know a law is coming up, and so buy a stock that is going to benefit from it: your argument is convincing there. But they might also hold a stock, and because of that they might feel more strongly one way or the other about a particular law: that feels like a problem to me.
Unfortunately there is bleed through between these, and no good way to distinguish the two except ok a case by case basis, which seems to me like a credible argument for forbidding all trading.
My sense is that this is one of those feel-good things, like setting politician salaries to a low level, which doesn't actually do anything to improve the quality of government.