What is ungrammatical about "I have to be home by 4" or "I've got to be home by 4"?

i misstated myself. i didn't mean to suggest that it is poor grammar, when this quite obviously *is acceptable usage. what i intended to say was that it seems strange usage of the word "have"; to my [limited] knowledge, none of the romance languages would use the verb root "avoir/tener/etc" to imply an imperative, but rather solely to indicate possession.

my query was simply how "have" came into this particular usage, not whether or not it's now grammatically correct. (sorry!)