Is there only one lego Rohan soldier? Why? As far as I can tell, Lego has released only one set containing a regular rank-and-file Rohan soldier, that is Uruk-hai army.

Is this correct? Why is it so?
This is correct. I double checked on the LEGO wiki. The reason is likely because they haven't had time to release more sets that take place in scenes where the Rohan soldiers are present. If they ever release an Edoras, Minis Tirith or Battle of the Pelennor Fields set, perhaps there will be more.