You're right that most of the time we need non-trivial algorithms or visualizations for trees for it to be useful. If I ignored that it would be like wishing for a "general binary editor" because it would be so "powerful" and all data can be represented as binary.
I think, though, that there's enough common ground between the various domain-specific tree editors that some kind of useful intersection exists. Then the domain-specific tree editors would simply be plugins.