There is the extension https://github.com/ProfessionalWiki/AutomatedValues that ironically allows defining rules for automatic setting of labels and aliases based on statements. Could be worth a look nonetheless.

Not only P31, but also other statements can be used for the generic (default) description. E.g. P17+P131 (country+administrative unit) as a basal localization of localizable instances (geographic features, structures, events etc.), P403/P4614 (tributary of / basin) for watercourses, P2505+P177 (carries + crosses) for bridges, tunels, ferries etc., P4552 (mountain range) for mountains, P27+P106/P39 for people etc. Maybe, some generic international patterns for some classes of items can be created, and specific international patterns for such cases where the generic pattern would be ambiguous, or redundant, or where the universal patter is not able to select the most relevant statements. I mean a supralinguistic summary of basic statements, which would be automatically translated into individual languages. It is important that it is a dynamic translation, i.e. that every improvement of the template is reflected in all uses and translations, without having to fix and save all translations separately.

Commons :Wikidata_Infobox gives an univerzal reprezentation of whatever item in an infobox. Similarly, we need a script which gives an univerzal short summary of the most relevant statements in one line.