I too find scopes or red dot sights rather out of place aesthetically on double guns but recognise that they serve a purpose for those with compromised eyesight, as I have.
These sights are generally fine on bolt actions as we have all grown up with this concept and a rifle today with just iron sights is more the exception than the rule.

The worst aspect of scopes and red dot sights is how much they affect the carry-ability of rifles and doubles in the hand. I find it is always nice to carry and handle shotguns without the adornments of scopes etc., and when hunting buffalo, my English safari sighted Mauser 404 was a joy to carry and use but alas my eyesight required something better as time went on. First an OEG red dot was fitted then later an EER pistol scope took the red dots place. Both these sights worked well, used with both eyes open although the pistol scope can be used one eye shut if preferred.