While calling it surgical is technically correct, "surgical" elicits imagery of a sterile environment under anesthesia, which is unfortunately not the reality. While post operative analgesia is sometimes employed, there is no legal requirement for it, and it is generally accepted by veterinary organizations and even by practitioners to be a painful experience for the animals. Another Wiki quote: The New South Wales Department of Primary Industries states in the Standard Operating Procedures that, "While the operation causes some pain, no pre or post operative pain relief measures are used." That being said, from what I can gather, post operative analgesics and antibiotics are increasingly popular ESPECIALLY with recent public outcry.
I think we see a lot of conflicts like this in animal agriculture; no one performs procedures like this "just because." Dehorning, debeaking, detoeing, mulesing, etc. can be extremely painful for the animal - and is also done for practical reasons, namely to address problems created by either by how we've bred the animals, how we're raising the animals, or how we're transporting the animals. It's a Catch-22: to maintain adequate productivity and keep up with demand, we do things like breed sheep with excessive skin folds, high wool production, and wool that does not shed on its own, but these exaggerated traits cause serious and possibly even life threatening issues that need to be dealt with - and the method of dealing with it has to be reasonable and economic before humane.
Now, I've volunteered at sanctuaries and been to privately owned hobby collections with large sheep populations, including breeds flystrike is more common in. And those sheep were simply kept clean and sheared and never developed flystrike. However, if you are an industrial operation with a huge herd and are looking to produce wool rather than just have sheep, keeping them clipped short is not practical, so to prevent financial losses...
Personally, my (granted very idealistc/unrealistic) solution is to simply not employ breeds who require painful mutilations to prevent health problems promoted by extreme anatomy. But that would mean either ceasing the usage of wool or accepting much lower yeilds and much higher consumer pricing. Basically: it's not a situation with an easy or practical solution for sheep, farmers, or consumers - which unfortunately is increasingly the case as the demand for animal products rises and intensive farming methods take over traditional farming methods.