That looks like the City of Detroit, not its suburbs, though I'm sure some of them do suffer some decay, in general Detroit's suburbs are pretty healthy.
The definition of 'suburb' has been changing over time. I can't speak to Detroit but for instance with Boston the original 'suburbs' would now be described as "the city of Boston, not its suburbs". Likewise the town I grew up in as a kid (mumble) years ago, I would have been laughed at for calling it a 'suburb' of Boston as it was too far out of the city. Now Wikipedia calls it a suburb of Boston.
I can speak to Detroit, and it's the same. The areas south of 8 Mile but not downtown would by definition be "suburbs" (and structurally resemble the outside of the city), but I'm used to people reserving the term for outside city limits. Now that I'm in Nashville, "suburbs" seem to usually still be inside the city, so I'm guessing it changes as cities grow/decay.
Nashville has experienced really rapid growth too over the last 20 years, and I think it takes a while for naming conventions to catch up. Given by the fact that what people call suburbs appear to you (as I'm assuming, a relative newcomer) to be "inside the city".
My own hometown has experienced rapid growth over the same time span as Nashville, and has annexed large portions of what were commonly known as the suburbs. So there has been a literal change from what used to be suburbs to now be within city limits, in the course of a generation.
