Declawing cats is done for owner convenience, to protect owners from scratches and protection of property. The surgery is not complicated and most cats recover with minimal side effects. The surgery is done by some veterinarians for the owner's health and/or to keep the cat from being euthanized. Declawed cats should be kept indoors, although many may become indoor/outdoor or outdoor only cats.
Declawing dogs are not generally done. The anatomy of dog toes is different than that or cats making the surgery more difficult and more likely to have poor results particularly in dogs over 10-15 pounds (cat size). Dog claws are essential to distribute the weight of the dog over the anterior part of the foot and for normal movement.
Amputation of affected toes (not all toes from all feet) is used as a treatment for some types of trauma and tumors in dogs. Removing the terminal bone with attached nail (declaw) is used to diagnose some tumors. Removal of just the terminal bone often results in infection with repeat surgery to remove the entire toe. Infection, pressure necrosis of the pad and long term lameness are reported.
One study of toe amputation that removed one or two digits on one foot as a treatment for localized malignant tumors reported lameness that lasted for over a month in all treated dogs and permanent lameness in 30% of the dogs (n=11).Only about 10% had recurrence of the tumor and the overall outcome was considered a satisfactory alternative for amputation of the entire limb (often used to treat tumors of toes).
There are a few reports on the internet of dogs that have had all toes amputated to control property damage (scratched wooden floors), for owner convenience (avoid scratches).
You've tried some of the alternatives. Clipping nails in dogs is easy although many dogs try to convince owners otherwise. Plastic nail caps are effective at preventing scratching. Carpeting can protect wooden floors. Dogs can be trained to stay off furniture and kept out of specific rooms. You mentioned the scat mat. Invisible fence has an in home system that works well to keep animals out of specific locations.
The short answer to your question is that surgical techniques for declawing either front or front and hind feet on dogs are not safe for the dog and frequently produce infection and permanent lameness.
Let me know if you have follow up questions.