I wouldn't blame the library for Seattle's more general problems (income disparity / regressive tax setup, high cost of living, homelessness, drug use).
The porn use is a bit disgusting, and segues into some freedom of use topics - FWIW in Austin they sorta solve this by having separate 'unfiltered' computers with recessed screens. In seattle they seem to solve things by having separate computer areas between adults and kid areas.
As for library bathroom issues, Seattle libraries have been doing things to make them less inviting to wrong folks by making the sinks shallow, removing paper hand towel racks, etc. It's arguably a hard balance.
Anyway, if you get past these issues the Seattle libraries are pretty impressive compared to many other towns. The Seattle downtown library top floors are great for getting work done, and many other branches have quiet areas. The online access of e-books/audiobooks is also fairly vast.