Yes it makes sense a bit. Many popular convents operate on 3x3 kernels. But the number of channel increases per layer. This, coupled with the fact that the receptive field increases per layer and allows convnets to essentially see the whole image relatively early in model's depth (esp. coupled with pooling operations which increase the receptive field rapidly), makes this intuition questionable. Transformers on the other hand, operate on attention which allows them to weight each patch dynamically, but it's clear to me that this allows them to attend to all parts of the image in a way different from convnets.