I apologize for bumping this old topic, but I have done quite a bit of research on this, so I want to share my experience.
Before you cover anything, be sure that you can safely do so. Read the owner's manual as some cars have airbags or airbag sensors in the seat, and that can be a problem when covered. Make sure that you buy good covers that fit your make/model, and will work with any seat-mounted airbags. If you have sensors in the seats, I do not think the car seats can be used, nor would they be effective with heated/cooled seats.
FWIW, I have never covered the seats in my cars, and have never had tattered seats, and I do have dogs. However, my dogs ride with a harness seat belt in the back of the car, or while secured in a carrier in the rear hatch area of an SUV, never loose in the vehicle. I do have a rear seat cover that comes in handy when positioning a wet dog in the back of a car, and I have a custom mat in the cargo area, so that protects the carpet. The cover is specifically designed for pets, so it is of much stronger material than many car seat covers.
I am told you need to be wary of cheap seat covers
https://wheelstips.com/best-car-seat-covers The buckles can come loose and then you sit on them and damage your leather seats. Also if the seat cover becomes damp for any reason you need to remove it until it and the leather seat is completely dry and clean. You need to check the seat covers regularly to determine whether they may have gotten damp without you knowing. Otherwise the seat cover can destroy your leather seats by trapping moisture against the leather. Finally I am told you do not ever want to cover only one seat. If you do, the seats will fade unevenly and will appear mismatched. You may also find after keeping the seats covered for 15 - 20 years they no longer match the other leather covered items in the vehicle and will appears as though they are replacement seats that do not belong in the vehicle. It was suggested if you want to keep all components of the interior of your vehicle matching, you remove the seat covers while the vehicle is parked so the seats will fade equally with the other components of the interior. You can re-install the seat covers when you return to your vehicle. Since you are not in your vehicle more oft than you are present in it, you should be able to ensure the seats fade equally with all other parts of the vehicle and will continue to match the interior.
