Medieval-esque phrases like "habeo abire" and "is habet scire" do not break the rules of Classical Latin, but I know that they were much more common afterward. This construction interests me greatly, because it's yet another "weird English thing" explained. However, as you might expect, it's quite difficult to search through an online corpus (if only corpus had a different accusative so that I could do a "or shall I say" thing) when the word habere has so many meanings. So my question is: how was "have to" used before the Middle Ages? Was it recorded at all? When was it first encountered? What were the opinions on it's usage at the time? I wouldn't consider these as multiple questions, but rather as suggestions for the ways in which one could answer my question.
There is a lot of material for you in the Thesaurus Linguae Latinae, VI, 3 ('habeo') col. 2454, 53 sqq., in col. 2455,65 sqq. also for the future (which might correspond more to the English 'I have to go' etc.). The secondary literature given in the TLL is probably outdated by now, but the examples are valid.