LA currently has about a billion dollars of outstanding general obligation bonds (edit: but that does not include all their future liabilities). They're still rated AA, but I presume that is because the credit writing agencies understand how many untapped revenue streams LA has, but again, those will require unpalatable political change. You can’t keep refinancing forever.
Philadelphia, Miami, and Chicago are getting close to junk bond status, and when that happens, the option to refinance starts evaporating very quickly.
My point is that much of what the city can tax has little to do with the city's GDP. Either the landscape of the city will have to change or the current taxation paradigm will have to change.
Again, putting $1B in some perspective, the LA Unified School District budget (which is county-level, so not directly comparable to the city, but anyway) is just under $19B. Maybe someone else can ballpark how much of that is associated to the city. Or look the other things that scale with population: police, medical, waste, etc.
LA is fine.
The city has a billion dollar deficit right now. Trivial for residents to afford ($83 per person), but difficult to actually implement politically.