The terrible problems of Detroit have several root causes.
1) Detroit was dominated by one industry (automotive). In contrast, other cities like New York, Chicago, Los Angeles, and St Louis had more diversified economies. They had several manufacturing industries, finance, chemicals, energy, etc. So if one experienced a downturn, others could pick up some of the slack.
2) That one industry was extremely hit hard by foreign competition.
3) Detroit had posionous race relations which doomed the ability of the civic community to work together to address long term, systemic problems. Previous ethnic groups used the power of patronage to build their own communities, but they did so in times of growing economic success and did not have as bad experiences. When Coleman Young became mayor and tried to the same, it was at a time when the monoindustry which provided the back of economic growth could not provide the growth needed to subsidize another interest group. They placed local politics from "we deserve the part of our share of the pie" to "we want our share of the pie to come from your slice".
4) The extensive special interests of the area made it very hard for Detroit to change policies to address these areas. The corporate culture of the Big 3 was established in times of industry dominance, and they could not adapt quick enough to changing economic conditions. The unions were interested in protecting current jobs instead of understanding the need for flexibility to keep their companies competitive. Politicians wanted to raise taxes to pay for promised benefits instead of finding ways to grow the economy long term. Civil rights organizations approached economic issues of revitalizing their communities the same way they approached dismantling legal barriers even though they required completely different approaches.
What other major city in America had these traits? Not many.
Seattle's economy was heavily based in aerospace, but Boeing only had one major competitor who did not threaten its dominance in the same way the Japanese auto companies did the Big 3. Nor was it was racially divided as Detroit.
Chicago had some of Detroit's attributes, but ultimately had too diverse an economy to decline as bad, and no single racial faction could dominate the city.
New York had major problems, but was revived by the rise of the financial industry in the 1980s, and had two strong mayors in Ed Kock and Rudy Giulani who reversed the decline.
Houston initially declined with the end of the oil boom, but recovered because as a newer city it has fewer political factions with entrenched rent seeking, so the lower regulations enabled diversified growth from the bottom.
There are a whole lot of smaller cities in a similar situation to Detroit - Buffalo and Newark come to mind - but they aren't as prominent as the largest US cities.
