If there is a tooth root abscess it is very wise to have the affected tooth extracted. Although the tooth itself may appear to be healthy the root is already compromised.
Once you treat the current Abscess with antibiotic's another abscess will probably return unless a curative treatment, such as a root canal is performed. Root canal's are rarely performed in pets since the procedure is more complex than an extraction, and therefore much more costly. Antibiotics are rarely effective for tooth root abscess's because the infection is trapped beneath the tooth and there is no ready access for drainage, unless a hole is surgically placed to allow drainage. Sometimes the abscess is so severe that it creates it's own hole by bursting through the skin of the face to facilitate the bodies ability to remove the infection.
Your vet is probably correct in wanting to extract the tooth. If the tooth roots are abscessing it means that they may be in the process of dying anyway, and therefore acting as a nidus for infections that can circulate and spread to the kidneys, leaflets of the heart, etc.
If you do have the dentistry performed please advise the vet that you would also like preanesthetic blood work performed on your cat. A complete anesthesia profile, including blood work is necessary to determine if anesthesia is safe for your cat, and is well worth the additional cost.
I'm also curious about your question.
My husky just chipped his k9 tooth and after calling around, I found out it costs $500 to extract it and $1200 for a root canal. It's not infected yet, but I imagine it will be soon because you can see the pulp.
I wonder how your vet can tell your cat's tooth is abscess
One thing I did learn is that sometimes teeth changes the structure of your pet's mouth and infections could be harmful to kidneys. I'm not a vet but I am wishing I could find a less expensive treatment.