Seattle's problem is exacerbated by the fact that the city has effectively legalised heroin, crack and meth by raising the bar on possession, and the police have a catch and release policy, without any actual treatment given. Numbers of addicts living here are also up because neighboring cities' police departments will issue non-extraditable misdemeanor arrest warrants for them, effectively turning Seattle into a dumping ground.
Not unique to Seattle or the US, police don't to waste their time on minor crimes. E.g. <$1000 in theft/damage, when a shoplifter fights store security but doesn't use a weapon, etc. This is because they know the county prosecutors will not file felony charges. Thus criminals target accordingly without fear of felony prosecution. I highly recommend this Reddit post by an anonymous Seattle cop explaining this.
Washington state also trails the nation in mental health treatment and has a high prevalence of mental illness. (Reference.)
I grew up in Perth, and for 5 years lived in a relatively dangerous area, Carlisle, between the Burswood Crown Casino and notorious Oats St Station. I felt unsafe on public transport more frequently than in Seattle, but I downright dread downtown bus changes where homeless people congregate. Overall, I would say I feel unsafe here enough that it is a major con of living here, and it's something I am forced to warn visitors, or prospective migrants about. Sorry Seattle and America - get your things together and help your fellow man like lots of other countries manage to.