Surgery has risks. Any surgical procedure has its risks/benefits. If the tonsils are too large causing problems such as breathing/swallowing and/or recurring severe infections, surgery may be needed. Depending on the health of your child, surgery may not be appropriate at this time and thus doc is advising you so. Talk to your doc and ask why etc...Learn about it so u can ask good/useful questions..Good luck.
It is safe. You were given bad advice.
Relative risks. In well trained hands (surgeon & anesthesia) this is relatively safe. Yet the procedure is not done on a casual basis like it was 4-5 decades or more in the past. Data show little or no benefit from incidental tonsillectomy as it was once done. Insurers are not going to pre-approve it unless it meets specific need criteria.