Can we find a rule for which the network looks (at least somewhat) like a real road network? Here are some simulations by Yucheng Wang.
Simulation 1 uses the rule for the Relative neighborhood graph, applied at each step to the newly arriving point. The resulting network looks very unrealistic, in part because there are many near-parallel lines. Seeking to avoid that issue, Simulation 2 modifies that rule by applying the new edge only if no other edge on either point forms an angle < 15 degrees to the new edge. Simulation 3 adds a new modification: if a new point is close to an existing edge then that edge may be replaced by two edges via the new point. Simulation 4 adds another modification: when a new point arrives, consider possible edges in the RNG, in increasing order of length, but only create a new edge (new node A to existing node B) if it has length less than 0.7 times the length of the existing route from A to B.
You can find more details on Yucheng Wang's GitHub page.