Native desktop/mobile apps that support simple formatting like markdown with an import/export function in either .json or (preferably) .md or .txt.

A simple tagging system (also in a simple format like .md or .html) is a nice feature. 1-2 levels of board-style organization/visualization is also useful.

Import/export is key - I just transferred all of my google keep notes to .md via pandoc and it was a pain. This functionality also addresses a lot of the sharing issues at a simple level - you can send or text .md files, for example, or work on them in a shared dropbox file.

Turtl comes very close to this for users interested in secure note-taking. Something like typora or remarkable with google-keep style organization/visualization would take care of a lot of use cases. Basically a simple markdown editor with better display/organization features. Really nailing math, table, code snippet, and image support would cover a lot of use cases.

Unless you really want to go hard in the paint on security, the app itself should probably focus on easy composition and attractive visualization/organization of the files.

Should be a native desktop/mobile app, lightning fast, support basic text-based formatting (e.g. markdown or simpler). Storage should be a file that can be put in Dropbox/Drive/etc for sync. And more important, free and open source.

The thing that is keeping from moving to Google Keep from Evernote is the web clipper. With Evernote I can easily clip a page (automatically removing the sidebar and other things not relevant to the article). That takes precedence over everything else that you listed.

IMO, easy-to-search, easy-to-organize, vendor-free and cross-device sync would be important.