"You shouldn't put an old dog or cat through surgery or a dental procedure." FALSE!
While there are some older pets that would not be stable to go through an anesthetic procedure, in general most older pets will do fine. In fact, our pets are living to older ages largely because of improved preventative care such as dental cleaning. In addition, an older pet may still have months or even years to live, so conditions that affect quality of life such as severe dental disease should be dealt with.
If your pet is having a good quality of life at its current age, then there is no reason to think it wouldn't be able to achieve that after many or most surgical procedures. In many cases, their life quality may be even better.
Today we have the power to treat perioperative pain safely and well. We can use safe anesthetic protocols along with careful monitoring under anesthesia. It's never been a better time to be an older pet!
For more information regarding anesthesia and dental cleanings, you can visit our friends at VetStreet: http://goo.gl/GLxT2o