In Canvas Announcements, will there ever be a was to prioritize announcements so that the ones that are most important can be "moved" to the top of the list?
At this point, the only way to reorganize announcements is to delete and repost. Being able to move announcements, similarly to how you can reposition modules, would be extremely helpful.
Canvas is in the middle of a pretty big update to Announcements and Discussions; you can follow it on the Discussions/Announcements Redesign page. Most of the conversation that I've seen has been around the discussion tool (I think announcements were included in the redesign because the use the same code), so I think this would be a great idea to add in that forum! The Canvas team, particularly @Katrina-Hess, has been very responsive to the needs of the community, so I'd encourage you to post your idea on the Redesign page.