>One of my pet peeves is when people say they don't "have time for" something. Time is not something you have;
The "have time" phrase is an idiom[1]: a group of words established by usage as having a meaning not deducible from those of the individual words (e.g., rain cats and dogs, see the light ).
For the criticism you wrote about "have", someone else can write the same criticism about "take" in "taking the time". And the same defense can be used for that too: "take the time" is another idiom that must be interpreted as a group and shouldn't be logically parsed as separate words.