You've also called out Watertown, Arlington, etc as modern American suburbs before but their density ranks well above major cities. But that's because they're not modern American suburbs. They're classical Streetcar Suburbs that predate the car and that's a very different thing.
IMO, there's zero doubt that Arlington and Watertown are suburbs of Boston by the most reasonable definitions of the word ("a. an outlying part of a city or town
b. a smaller community adjacent to or within commuting distance of a city")
However, if you continue to object to calling them suburbs of Boston, then look at Carlisle, Dover, Lexington, Lincoln, Sherborn, Sudbury, Wellesley, Weston, Winchester, and on and on. None of those Boston suburbs are even hurting for money, let alone "insolvent".