But R for run or right isn't arbitrary, nor is TAR for sailor: in each case it is a genuine usage or abbreviation which is being used in the crossword. They exists in the real world too.
Yes, it's real, but to stick the word "run" into the clue, so that people will know they need to stick an 'r' somewhere in the solution is incredibly far-fetched! That's what I mean by contrived. If you don't know the conventions, it seems to be impossible to solve the puzzle.
How do people learn the conventions in the first place?
'Short English thanks for a refreshing drink'.
See, this is what makes it so confusing for me. "Short English thanks" makes "tea" if you see it as a letter-puzzle, and "refreshing drink" makes "tea" by definition, too - but under no circumstances can you define "tea" as 'Short English thanks for a refreshing drink' - the clue doesn't make sense to me.
Parma, we do have a sort of cryptic crossword, and I like them better than normal crosswords, which just ask definitions, but ours are quite different from English ones. There are conventions, of course, and knowing them means you can solve the crossword more quickly, but you don't
need to know them to solve it - a bit of out-of-the-box thinking will get you there, too. My first one was given us by a teacher at school, and we could solve it without any pre-knowledge. They are usually called "Tricky crossword" and they are supposed to be amusing rather than just hard, and the clues often rely on puns and word ambiguities.
I had a look at one and even found a clue that works in translation, because the solution is English (there
are harder clues, this one is particularly easy): "Hilary was that kind of lady".
Another funny kind of puzzle is a kind of "Silbenrätsel" (not sure if there's a name for it in English - it's not a crossword, but just a list of words to find, and all the syllables of the words are given in a list on top) - in this puzzle compound nouns are given misinterpreted definitions, for example "war horse that is part of the artillery", or so.
The hardest puzzles I've come across are those that just give a list of clues, but they are not in the right order, so in addition to answering the clue you have to figure out where in the crossword it goes. This only works if you can answer
all the clues, of course, and as they are always ordinary definition clues, I can never answer them all.
The guy made the puzzle, had this dorky word combination, was too lazy to fix it, and DROVE ME CRAZY. 
well, I guess it's an acquired taste.
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