I think you’re framing it backwards, in the title.

Nonaccountability is assumed to be a “right” intrinsic to authority, & the greater the authority, the greater the non-accountability.

THAT is the problem.

NOT that the most-authority has the least-accountability, but the WHOLE MECHANISM of accountability-only-for-the-bottom-nonauthorities.

Class-decadence in the upper levels is the same mechanism.

Privilege means “inherent” nonaccountability, according to group-animal politics ( herds, packs, political-parties: it’s all the same social-mechanism ).

The ONLY method I can see for correcting this fundamental-political-fact ( of both left & right ), is to remove accountability from political-“will”, & put it in some automatic ( like decision-trees, or something ) mechanism, that doesn’t obey ANY social-pressure: it enforces against integrity-violations automatically.

There is no alternative: human-nature simply doesn’t have any spine/uprightness, therefore accountability has to be intentionally placed in automatic-mechanism, instead.