I find a discrete model of spacetime very attractive, for much the same reason given here; the real continuum is intuitively too big for space to run on it. I took an interest in the causal sets approach to quantum gravity for this reason.

However, unfortunately, there's simply no evidence for it. There's an argument that discrete spacetime would lead gases to heat up over time, but this hasn't been observed to happen, so either the discrete structure of the universe is pretty small, or it really is continuous.