Would be nice to re-implement "external overlay display" via Constant combinators so builder can label buildings with icons which cannot be crafted and put into the chest (e.g. liquids and gases).
Is this technically possible?

Yes, but to work, it would require a setting to be enabled that isn't enabled by default (Show combinator settings in "Alt-mode").

If that's a no-go to many players (I prefer having this flag toggled on), we might also provide a choice to the player by one of the options:
- remove pre-placed boxes and allow to place either a box or combinator in a factory;
- allow to switch between boxes and combinators by some kind of in-factory toggle (similar to input/output arrow toggles);
- subclass default combinator overriding Alt-mode behaviour (if that's possible);
- place both boxes and combinators (in groups by 4) in a factory and output either from one group or another (this one would look ugly and not clear to the player).

Does any of these ideas look good enough?