There seems to be an implicit assumption behind the tax rates argument that municipalities are essentially commodities offering identical/nearly identical services, hence there's a high-responsiveness to tax rates. In reality, things are more complex. People had been leaving Detroit where tax rates are high/tax payments are low on account of depressed home values for areas in which they pay higher taxes. But for them, the higher taxes are well worth it, because they are getting far more marginal value in the form of better schools, better services, greater safety, more employment/career growth opportunities, among other things. They're willing to pay more in taxes to upgrade the quality of their life.
The hypothesis that tax rates doomed Detroit is essentially the same as an argument that when stores charge higher prices, shoppers will only go to the dollar stores or other deep discount stores. That doesn't happen, because high-end stores offer sufficient extra value (more features, more service, more generous warranties, often more durable products, greater convenience, a more pleasant shopping experience, etc.) that makes it worthwhile for shoppers who have the income/finances to pay more to go there. Differentiation does exist and consumers are willing to pay for it. The same dynamic exists with regard to municipalities. Hence, the seemingly irrational decision for people to willingly pay higher taxes is a wholly rational one once the added value from their relocation is considered.