First, the grandfather paradox isn't real. All you do is get Buddhist with it. The moment is all that exists; time is just a way of tracking configuration permutations within the moment. Hopping out of one moment and into another, without travelling through all the intermediate moments, already suspends the allegedly tight coupling between time and chains of cause and effect. The grandfather paradox is for people who've never bothered to read quantum physics.
Second, while time may not truly exist in the classical sense, air certainly does. In normal life, when we travel from moment to moment, we can move into a new physical location by pushing air out of the way. If you suddenly appear somewhere because you've travelled through time, you suddenly share space with other matter. Although you might not, which brings me to the third issue.
If you're on a planet which is rotating about its own axis and rotating around the axis of the sun and located within a solar system which is itself moving through space at 45,000 miles per hour, then any time travel system would have to involve a lot of travel through space as well, unless its only purpose was to cause people to die horribly in the most scientifically impressive way. Because ten seconds ago, the entire planet was somewhere else. So if you push somebody into another point in time without also changing their physical position, they'll probably just be stranded in the vaccuum of space.
Like anything else, a practical time travel system would have to solve a lot of theoretically unrelated problems in order to be even slightly useful. And most of the "oh wow man that shit is deep" that goes on around time travel stories is just not.