"According to any textbook, the present tense of the verb drive is drive. Every junior high pupil knows that. Yet if we say, 'I used to drive to work but now I don't,' we are clearly using the present tense drive in a past tense sense. Equally if we say, 'I will drive you to work tomorrow,' we are using it in a future sense . . . In fact, almost the only form of sentence in which we cannot use the present tense form of drive is, yes, the present tense. When we need to indicate an action going on right now, we must use the participial form driving. We don't say, 'I drive the car now,' but rather 'I'm driving the car now.'"
- Bill Bryson, from The Mother Tongue: English and How It Got That Way
Bryson observes that present-tense inflections of verbs are more often used to describe events in the past or future than in the present. But surely this is simply because we rarely have cause to describe the present we are physically speaking or writing in (or the present we expect a reader to be reading in). The relevant present for most accounts put into words is either the one we have already lived through, or the one we anticipate.
We don't say "I drive the car," because we don't need to. We do, sometimes, need to say "I did drive my car to the airport and I did leave it there in an egregiously expensive parking lot."
Using the present-tense verb inflection in a past tense statement conjures for the reader or listener a sense of a present unrolling at the same rate as the story. It transposes the audience backwards or forwards into the narrative present, which is the one that matters more than the present the speaker/writer/listener/reader inhabits in "real" time and space.
(This is even more true for past-tense and future-tense construction of the present participial form (driving), which is perhaps used even more than the simple present tense infinitive in storytelling.)