Edentation, or the removal of all teeth, is a common solution to feline stomatitis when no other solution can be found. My experience with it has been entirely positive, and I've talked to several cat owners who have also had cats with stomatitis who have removed their cat's teeth and no one has ever said to me that they regret the decision. It's a relief to know that my cat is no longer in pain from eating.
Here's my experience:
My cat, Hunter, had mild stomatitis for several years when it suddenly flared so badly that his gums looked like balloons. We treated him with antibiotics (which reduced the acute flare), and then spent a few months trying several different experimental treatments my vet found in veterinary journals. Nothing helped, so we had his teeth removed.
It's been about two years, and he's been back to the vet twice for his mouth. The first time, we noticed that once the swelling in his gums went down and everything healed, he had a bone spur on his jaw. It never would have become an issue if he had his teeth, but it was poking through the gum tissue and causing irritation, so the vet opened his gums, filed it down, and stitched everything back together.
The second time, a small root was surfacing. It had probably broken off during the extraction (which was done by my general vet, not a dental specialist). The vet was able to get it out with only mild sedation (not full sleep).
His mouth is leaps and bounds better than it was, no redness or puffiness at all. He eats food just fine. He drops it a little more than he used to, so the floor is a little messier, but he'll eat a whole meal at once rather than a bite or two and walking away (we assumed that was because his mouth hurt). We feed wet and dry, and he has no problem with either.