Is it really that dangerous?

"Key medical objections to infant anesthesia - that it was (a) unnecessary and (b) dangerous - were resolved by the brilliant research of Kanwal Anand and colleagues at Oxford from 1985 to 1987. Making precise measurements of infant reactions to surgery, they proved that the babies experienced pain, needed and tolerated anesthesia well, and had probably been dying of metabolic and endocrine shock following unanesthetized operations."

Source: http://www.nocirc.org/symposia/second/chamberlain.html

I'm not a medical doctor and not necessarily current on the latest research. However, there is quite a lot of evidence that general anesthesia is fairly likely to cause actual brain damage in infants and young children [1,2] with significant consequences in later life and there are (less significant, but still non-trivial) issues with various methods of local anesthesia. As far as I know, there's a lot of unsolved issues in the field of infant anesthesiology and the general trend is to err on the side of caution.

[1] http://www.webmd.com/parenting/baby/news/20120820/anesthesia...

[2] https://www.fda.gov/ForConsumers/ConsumerUpdates/ucm364078.h...

If there is a need for "repeated or lengthy use of general anesthetic" on infants there is usually already something wrong which could attribute to the said symptoms as well. It would be crazy to not use anesthesia on young children based on this warning, as shock (Which usually happens when operated on without anesthetics and the reason the child is silent during and a while after the operation) may cause worse damage.

The first reference I linked specifically controlled not just for disorders that could lead to similar symptoms, but even things like the mother's socioeconomic status, etc. The effect was still huge.

I don't think anyone's seriously suggesting simply forgoing anesthesia in life threatening cases, but people might want to rethink a routine tonsillectomy or some dental work.