Why are stars still distant from one another?
The initial star formation regions were regions that have a high enough mass density to form a star. The density of the early universe was not constant at different locations. Some regions had high enough density to form a star, and some didn't.
When a star forms it draws in matter from a large distance away. This forms an accretion disk and leaves a temporary relatively empty space around the star at a large distance away. There is no way a star can form in this low mass region. Once you get further away from this region the matter density may return to a level where a star can form. But this region is far from a star.
Yes, gravity from a particular star is pulling at other stars but there are many stars pulling on the particular star of interest. So the net force on the star may be very small.