Why is peer-review for journals free of charge but not for other academic documents? Peer-review is an important part of decision-making in academia. Journal reviewers do not get paid.

BUT funding agencies pay for the same peer-review (of research proposals). OR universities pay the external referees for reviewing PhD dissertations.

My question is: if peer-review is voluntary and a professional duty, why isn't it the case in other reviewing processes?
BUT funding agencies pay for the same peer-review (of research
  proposals).


Not necessarily.


  OR universities pay the external referees for reviewing PhD
  dissertations.


Not necessarily.


  My question is: if peer-review is voluntary and a professional duty,
  why isn't it the case in other reviewing processes?


Because compared to a journal article, those are much more intensive. It may require travel, and almost certainly involves several days of work. Therefor those types of activities are disadvantaged in my considering of "Do I have time for this?"

The way to address that? Incentives. Including monetary ones.