Good day! Design loads (static, cyclic, impact, etc.) should include all the variety of external influences, and not just the loads of passing vehicles. For example, wind or earthquake, temperature cycling (within a day or a year) can determine the limiting state of the span structure, especially in the case of presence of flaws. Therefore, in your case, in order to neglect the real fatigue strength of the structure, you should prove that the possible cyclic loads are negligible.

You're assuming the use of this road and nearby community will stay the same and not change. Nor will anyone ever use it with a over-weight vehicle. I suggest your current design assumption could make you liable in the future. Please spend the effort to design for current and future fatigue. Think of it as being more sustainable. Even with changes in climate.