Any city with a massive decline in population (which was probably triggered by racial issues and bad governance in the 1960s, a time when a violent armed revolution, at least at the local level, was quite possible) is going to have problems. Detroit had a heavily union population, reflected in the government as well, so unlike mining/etc. ghost towns, the "hangover" from the massive decline in population was a lot more unsustainable (in a place like Butte, people just left when industry left).
Sure, the decline into a war zone hurt, and compounded all the initial problems, but NYC was a warzone in the 1970s/1980s too, and didn't die. LA and Miami in the 1980s/1990s. I mean, even Oakland is somewhat turning around now (largely on the strength of SFBA overall and an artificially limited housing market in SF, true, not internal improvement.)