The legal answer for why consular districts exist is that the Vienna Convention on Consular Relations specifies that consular posts are associated with consular districts, and a consular officer isn't allowed to exercise his functions outside his district except in special circumstances with the approval of the receiving state. Furthermore, a country can't unilaterally change these districts; they're established with the consent of the receiving state.
Consulates have duties beyond issuing visas and passports; their further duties include lots of things for which they need to work with local authorities (e.g. helping arrestees, acting as notaries, handling deaths, helping their citizens who are having problems). Notably, the powers of a consular officer technically don't include talking to local authorities outside their district; the receiving state is entitled to decide that local authorities only have to deal with the consulate covering them.
The VCCR likely doesn't prohibit the Russian consulate in Seattle from giving a passport to someone from Portland; you'd be physically in Seattle when you apply, after all. However, Russia can say that they'd rather someone living in the US long-term not jump around between consulates (for instance, because they want to keep their dealings with you under one roof, or because they budget assuming you'll go to your district).
As for why Portland is in the SF district: Russian consular boundaries lie on US state boundaries. Because a lot of the point of consular districts is dealing with local authorities, this makes sense. So, if Oregon is all in one district, the SF district isn't a ridiculous choice. Other countries split CA (presumably because it's quite big), but it's generally preferred to have consular districts line up with internal boundaries (and Oregon is not big, so is unlikely to be split).