"Can I tell you a story?"
As long as the Chinese sentence is acceptable. I agree with the first part. But I think this is not a good argument:
"If English could omit the 听, why couldn't Chinese?"
There are many cases were you can't omit something because it is just not acceptable/grammatical to omit it in a given language. You can already spot the difference in your English translation, because this doesn't seem like a normal sentence to me: "Can i tell you a story to listen?"
I get your point, but you should be putting it after the subject more often than not
This sentence comes with the 给你听 attached and isn't accepted without it. The one about daddy reading stories to the kids comes without it and doesn't work with it. Go figure. Can anyone explain the difference, or is it just one of those 多邻国 idiosyncrasies not to be taken seriously?