Kind of? Violent crime is always going to be higher in a city than the suburbs, that’s just life.
But homelessness…it’s rampant everywhere, although a different kind of homelessness. Think fewer tent encampments and more motor homes. There are RVs parked on El Camino for miles down Palo Alto and Mountain View.
Not, of course, on the actual residential streets, because the city made that illegal - which brings us on to the nasty politics, which I’d argue is worse in the suburbs than the cities.
I still think there is a difference here between American and Australian usage – American popular conceptions of geography pay far greater attention to local government boundaries than Australians do. That makes complete sense, considering that local governments in the US have vastly more power than those in Australia – here, courts, elections (even local elections), prosecutors, corrections departments, law enforcement, fire departments, ambulances/paramedics, public schools, public hospitals, public transport and land titles are all exclusively state government responsibilities, and in inner metropolitan areas, the state government runs the water supply and sewerage system as well. Americans pay much more mental attention to local government boundaries than Australians do, because those boundaries have a significantly greater impact on their everyday lives.
So if we're actually in San Francisco metro area and I talk about "San Francisco", I probably mean the city proper. But if we're in DC and I talk about "San Francisco", I probably mean the metro area. Or, commonly, I actually mean somewhere specific but I don't expect my listener to know the more specific areas, so I just say "San Francisco".
Not that I've ever lived there (fellow Aussie like you, just visited it for work) – but my impression is that some of those problems – especially the homelessness, crime and public defecation issues – are much worse in San Francisco proper (Oakland too) than in (say) Silicon Valley.
One language issue here – Australians tend to use bare city names to primarily refer to metropolitan areas – an Australian who says "Sydney" or "Melbourne" likely means the whole metro area, not the "City of Sydney" or "City of Melbourne" local government areas specifically – whereas to an American, "San Francisco" usually only means "the City and County of San Francisco", and the whole metro area is "the Bay Area". An Australian is likely to think of Silicon Valley as part of San Francisco, to most Americans Silicon Valley is not part of San Francisco, rather (roughly) 45 minutes south of it (maybe closer to 30 minutes from the southern end of San Francisco proper to the northern end of Silicon Valley).