Why light coming from distant stars is not discrete?

You are right that single photon detection is a discrete event. But you are under the false assumption that these "rays" are discretely distributed.

Ideally, a photon would have an equal probability of being emitted through any solid angle out of the star. i.e. it is a uniform probability distribution with respect to the solid angle. There aren't single rays that are evenly distributed around the star that the photons travel along.

For a water analogy, it is not like the star is a spherical shower head where photons can only be released from discrete locations. So, even if you might have a different random distribution of photon detection events at different angular locations relative to the star, you will still always see photons (this is neglecting stars that are so far away from us that their light never reaches us due to the expanding universe).

Of course, if you are far enough away you will experience fewer and fewer photons. However this is not limited to certain "rays". This will be true at any angle at a large enough distance.