Unpredictable as many phrasal verbs are, I think it would be wise to acknowledge that there has to be some underlying reason for the speakers of the language to have selected a certain preposition rather than another.
In his book "English Prepositions Explained" (Revised Edition), Hilderstone College, UK, Seth Lindstromberg carries out (notice by the way this use of "out" which I find to be related to the metaphorical use I will refer to below) an interesting analysis of some abstract notions expressed by prepositions, an enteprise he says was inspired by Dirven (1993). In his introduction to his Survey and Index of Important Abstract Notions Expressed by Prepositions, he states something I find to be of essence to really understand the matter:
The spatial meanings of English prepositions play a role in the expression and structuring of many key non-spatial notions.
Lindstromberg claims that the basic meanings of most prepositions are so substantial that speakers routinely use them metaphorically in order to make sense of non-physical experience.
On pages 39 to 42 of the mentioned book he explains the different abstract or metaphorical uses of "out", but the one that interests us appears at the very beginning, on page 39:
- OUT for extension/expansion beyond former boundaries
The author says that the physical meaning of extension or expansion that appears in examples like: "Melting butter spreads out" or "Unroll the roll of paper until it is rolled out" underlies the metaphorical use of "out" in several phrasal verbs:
I just mentioned "carry out", and there's also "find out". There's definitely something in the meaning of "out" that made it the right choice in the process of creating these phrasals, "sort out" included.
Other metaphorical usages of OUT according to this author (both the definitions and the respective examples are quoted from the book) are the following:
- Straighforward metaphorical usage of the basic meaning:
(39) Can any of your readers kindly help me out of a difficulty?
(40) I managed to talk Liz out of doing more housework.
- From the beginning to the end:
(43) Jo Durie is hoping her dodgy knees hold out for an emotional Wimbledon farewell.
Other examples of this meaning are drag out (a meeting) and talk out a problem.
(44) He's playing out of his skin to be honest and ... he's easily one of our most valuable players.
(This meaning of "out" also accounts for the existence of verbs like "outperform", "outdo", etc.)
Disappearance: be out (not in), go out, take out, die out, leave out, rule out
In the open, not hidden, understandable, available:
(50) People should learn to bring their differences out in the open.
(52) Figure/Puzzle/Work/Reason it out.
(53) My book is out -- sometimes good things happen...!
- Loss of possession or supply:
(54) He cheated me out of money that I'd be glad to have now.
(55) We're running out of time.