Unethical? Not!!!
This is a property management situation and not a listing contract. Those are two entirely different situations. Property management usually provides for performance by the mgr and are based on occupancy rates of the property in addition to other profit centers. If the mgmt company is doing little to advertise the vacancies in a property then they are not fulfilling their obligation to their clients. Often absentee landlords do not pay close enough track of the breakdown of their property.

I also have a landscape business and using your logic I would neve be able to contact any potential customer currently being serviced by another contractor because it would be "unethical"! That is a load of bull and you know it.

I have 3 out of state rental properties that are managed by others but I actually am an informed owner that watches my quarterly statement. If I were not I would be greatful to get a letter notifying me that my current mgr was not doing everything he could to keep my property occupied. The letter writer may not get my business but it will definately prompt a serious conversation with my property mgr and a review by my attorney to determine if he has breached his contract for management of my property. If he breached he is gone and if not he has till renewal to perform or the new guy will get his shot!