I think that's because of what we're talking about right now -- all of these workers heading to the big cities instead of living out in the suburbs. When the workers return to the suburbs, business will follow them, and they won't be insolvent anymore.
The suburbs around Boston are definitely not economically insolvent, and the ones in metro-west are fairly flush financially (continually building and upgrading schools and other town amenities).
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".
Source for that claim? I hear it all the time, but never a source that actually stands up to scrutiny. (strongtowns is the most common - they are not a source)