Downtown Seattle can be a bit rough. I wouldn't lay it squarely at the feet of the mayor though - a lot of it traces back to city planning gone disastrously wrong.
Just a few off the top of my head:
- the southern end of downtown is strictly commercial. Little to no mixed zoning here, meaning that as soon as 5pm rolls by the entire area is a ghost town. If you're there past 6-7pm you will see that the homeless and addicts move in to fill the void. There is no residential or leisure traffic to balance this out. This is US-style single-purpose urban zoning run amok. Vast portions of the urban core is entirely idle after work hours.
- downtown Seattle isn't a cultural or entertainment core, unlike the downtowns of most cities. The actual food scene, nightlife scene, music scene, etc, are in surrounding neighborhoods like Capitol Hill, Ballard, Fremont, etc. This contributes to low foot traffic after work hours, which contributes to higher crime and simultaneously a magnified perception of danger.
- poor urban planning decisions meant an explosion in large-scale development without sufficient requirement for retail frontage. Lots of buildings that take up the entire block with little to no ground-floor retail, making it a pedestrian dead zone and contributing to the feeling of walking down a shady alley no matter where you are. See: much of Belltown, where the declared intent was to produce a walkable neighborhood full of restaurants and nightlife - except few residential buildings wanted to play host to them. This has resulted in little pockets of activity with vast stretches of nothingness in between them.