It seems that adding Fresnel reflection/transmission makes the objects more opaque. Is there a reason for that?
I think the opacity of the object is actually a key factor Fresnel reflection would take place; if the object is completely mirroring all the light rays, the refraction part of the Fresnel reflection would not happen but just perfect reflection.
When we vary the amount of reflectance according to the angle of incidence, we are able to make the reflection more consistent with what we expect to be real shapes. Technically, for example, the edges of a glass ball are supposed to reflect everything, while a center would only reflect around 6%, according to the lesson here: https://www.scratchapixel.com/lessons/3d-basic-rendering/introduction-to-shading/reflection-refraction-fresnel
The lower, fixed reflection amount just makes entire ball look more transparent and less opaque, so from my understanding it seems like the increased adaptive reflection makes the ball as a whole seem more solid. The reflections in this image look very solid, which aligns with what the link above states, and also creates the visual effect you described.