I sometimes worry about the camera being too heavy for one of those sling straps, not because of what you said as I did not know that, but mainly because I would rather prefer to assume there could be something wrong with the idea. After all, the tripod hole at the bottom of the camera was designed for tripods not for sling straps. That being said, considering I do have a sling strap, I prefer to mostly cup my hand under the camera and give it a little bit of a lift, to use my arm as a support for the sling strap, let the camera spend a bit of time being carried by my arm in addition to being carried by a sling strap. I mostly let go of it when I needed both hands, like to open a bottle of water, to open a sandwich wrapping, to write notes, or whatever, then mostly go back to holding my camera when walking around.
Does it help? Does giving the camera a bit of a support from my free hand help ease off the pressure on the tripod mount? Aside from this, I do find it help ease off the pressure the strap is on my neck.
I have noticed a few photographers let their cameras hang totally by the sling strap while they walk around with their hands in their pockets.