It would depend on the anarchist you ask (how many of my answers have started like this?).
From my perspective if a person truly values freedom, autonomy, and egalitarianism, while opposing hierarchy and domination, then yes, a more primitive lifestyle is an acceptable trade off for anarchy. But that doesn't mean that I am living the dream, either, I am plugged-the-fuck-in to the computer in my comfy home in one of the most connected urban areas on earth. That is is an acceptable trade off is like a math problem (tips hat to Broner) that an insurance wonk or accountant would use: Does this column outweigh that one?. Just because it is acceptable doesn't necessarily mean it is desirable.
It might be, but I am skeptical of anyone offering up a solution or an end point we need to work towards. I find it much more helpful to be focused on the elimination of the state, capitalism, and civilization than on a sort of prefigurative politics, even if it is an anti-civ prefiguration. I want to be careful here though, as I am not trying to create a strawman, I think many who call themselves anarcho-primitivists feel the same way, and use that label, or focus on other aspects of resisting, such as rewilding. This is where it gets real messy.
Lots of anarchists, given the choice between the ever expanding misery of industrial civilization would say that a primitive lifestyle is "acceptable," but, at least for myself, I am not a primitivist. There is a difference between being anti-civ and being anarcho-primitivist. Anti-civ is about a critique based in negation, in knowing what we are opposed to, but doesn’t necessarily offer up solutions or programs, whereas primitivism is more of a positive vision of the future(primitive). At least that’s how I would categorize the differences. AP is anti-civ, but Anti-Civ is not necessarily AP.
Then again, there are plenty of anarchists would agree that what you call the “surgical approach” is more desirable. They tend to argue a couple of distinct (but related lines). First, Industrial civilization can be saved if the class structure of society is jettisoned along with capitalism, the state, and blah, blah, blah. This argument boils down to that workers who are deciding what they will work on will not willingly do things that decimate their world. Since most of these anarchists tend to argue for some form of global networking that replaces the capitalist system of globalization, obviously we would all take in to account the needs of everyone else.
This is frequently supplemented with an argument that without the profit motives inherent to capitalism, green technologies would be allowed to flourish and develop in ways they are not currently. Electricity and materials would be generated without the use of petroleum products or nuclear power, commodities would be made sustainably, and so forth. I’ve gathered it would be something akin to a governmentless version of the world described in Ecotopia by Ernest Callenbach.
Even if we did maintain green technologies that would do nothing to deal with over-population (which in turn creates more issues for industrial civilization), with the alienation we experience from the world around us (including the people around us). This part of my beef with pro-civ anarchy is highly informed by anarcho-primitivism (in specific John Zerzan’s “Origins” essays). Frankly, I don't think that a globalized network of green industry is possible without government, but this is an argument that is put forward.
Related to part of your original question that I didn’t previously address, things such as level of comfort and relaxation are relative, and certainly, our current level of comfort and relaxation are predicated and maintained by the imiseration of billions of other beings. And industrial capitalism leaves me feeling hollow. I want to destroy it because of how it hurts me, and how it hurts others similarly, and I want to destroy it completely because it so completely colonizes my life.
Some further things that would be worth your time to look at: