In the Public sector, the demonstration of project management skills/education/expertise is valuable and well taken into consideration in career advancement /progression. The structured recruitment process requires proven experience that is focused mainly on the strategic area rather than the operations; this comes along with management of budget and human resources that are usually done by project managers and are always in high demand.
The mindset of project managers, especially from the agile space, and executives differs. In order to climb that ladder, you have to be savvy in politics, which many PMs do not like (though it would help them to influence stakeholders).
PMs that expanded their capabilities towards an executive mindset is indeed PMO Leaders, but also portfolio managers and program managers, all of which succeed in a more undefined environment.