Some modules have a LOT of labels, so isn't there a danger this becomes very unwieldy? Also, how does it interact with the multi-language resource files? Does the override beat the resx, regardless of language? Can the overrides cope with multiple languages?
I'm thinking that changing labels is really the same thing as localisation... i.e. it is adapting the presentational description to use the words that best match the cultural and linguistic world view of the admins and users. So your "Tagged in:" might be my "Indexed as:". Both "en", but both legitimate localisations.
If this is valid, then could we look for a way of allowing the localisation to persist through upgrades? The skin is a good place for this as Isaac suggested. So, could this be achieved by a setting at the site level along the lines of "Use skin-specific resource files?" = true/false. If true, then when rendering any feature, we look into the skin folder (or a resources subfolder) for the relevant setting in the resx file, and fall back to the normal files if not found.
This would allow me to change every label in a way that survives upgrades, and works across all languages. If an upgrade adds new labels, it will still work as it will fall back to the default.
(PS I'm feeling something similar could work for email templates, which are also blown away by upgrades, and frequently need customising).