Why do you suspect the crypticness of the puzzle's language is the problem, rather than the fact that a large portion of people haven't studied basic logic and are thus unable to complete basic logic puzzles?

It's not just a basic logic problem - it's a language translation into a logic problem problem. You have to 'get' that is what you're dealing with.

Incidentally, I get a similar feeling from these puzzles that I get from code questions or examples where every variable or function is named 'a' or 'b' or 'foo' or 'bar'.

(aaand I just had a mini-epiphany of sorts that when I see those types of programming puzzles I should probably write them out and substitute the variable names as I go....)

Actually, it's the opposite. It's a translation of a pure logic puzzle into natural language.

Firstly, someone reading the puzzle needs to grok that some of the day-numbers are unique across the months (e.g 18) and some are not (14). Then they need to grasp the basic dynamic on the situation, e.g. that if Cheryl's birthday had been May 19 then Bernard would have known straight away.

If you dont initially grasp the above then Albert's initial declaration "I don't know when Cheryl's birthday is" just seems to be a redundant statement that doesn't offer any information. And thats just the first hurdle of the puzzle.

A lot of people hate maths-questions-stated-as-stories, even simple ones ("There are several chickens and rabbits in a cage (with no other types of animals). There are 72 heads and 200 feet inside the cage. How many chickens are there, and how many rabbits?" etc etc) so to people like that, this Cheryl-birthday problem initialy presents as hopelessly cryptic.