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The USA is clearly not prepared to sacrifice any of its own cities to prevent an invasion of Taiwan.
All this sabre rattling and military buildup only serves to put money in the pockets of the military industrial complex and/or build military capabilities for each country to exert its will within its own sphere of influence.
I think there are 2 false statements here. First, you could have conventional conflict alone, the same way you had WW2 without extensive use of chemical weapons.
Second, there are possible paths to have a winnable nuclear war, actually, the US did have one a couple of decades ago and it won. I do agree that saying this out loud though is dangerous because the reason for nuclear taboo is also based on the perception of "end of world" it has.
Modern nuclear weapons seem to be very effective, but as you note, it has only been tested once (when only one side had them).
Well yeah because at that time they were the only one who had a nuclear bomb. That situation didn't last long.
I think it's really great that it's such a taboo, otherwise these things would be used a lot, incurring all sorts of pollution, mass casualties and chances to escalate. It's a good thing that these have not been used since WWII though I do think their existence as a deterrent has brought us a bit more peace.