Description of the need
When adding a context by path, every field available to the context is presented in the dialog box. This not only produces un-necessary clutter but creates a bad UX because the field chosen may be attached to a different entity type, making it easy to accidentally add a similarly named field that won't display data as expected because it doesn't belong to the given layout path provided in the context.
Additionally, not filtering on a given criteria might also a performance hit on larger sites that have hundreds of fields. By limiting through the selection rule, it reduces the number of fields that need to be loaded.
Proposed solution
Add Selection Rules so a context can be limited to only show the fields related to the rule.
Alternatives that have been considered
See the Drupal Panels module Selection Rules for more inspiration.

Recent comments
@yorkshirepudding thank you for the additional info on improving discoverability and a handy way to keep a list of projects for reuse.
Why not add a Github star?
It is a good point @izmeez and when I was researching repo discoverability I found that GitHub search does prioritise matches with more stars. This is what I was researching for:...
Why not add a Github star?
Do you have a separate development environment and transfer database and config between sites?
Wierd happenings regarding updates...