Spontaneous crack healing due to van der Waals forces is an important phenomenon in diverse areas such as precision assembly, locomotion, soft robotics, and micro- and nanomachines. For rough surfaces that can be described as a collection of asperities, parallel plate models are used to gain insight into the adhesion values. A single adhesion value is then found for a given surface description. However, experiments reveal a range of values. Here, implementing a simple beam model to gain physical insight, we show that an important contribution to the range can be due to the placement of asperities relative to the crack tip. For example, tall asperities far from the crack tip resist crack healing if they contact the substrate, but promote healing if not in contact with it. Due to this effect, the beam model predicts a range of values that is significant compared with the observed experiment variation. Furthermore, as the crack approaches mechanical equilibrium, the resisting action tends to dominate over the healing action, and the beam model predicts a lower adhesion value than the parallel plate model. These effects will be greatest in the case where the elasticity (Tabor) parameter is small.