Krinkle,
When you say "Whether some Wikipedia's output is semantically correct is important, but (afaik) has *zero* relationship with Wikidata. And as such is not relevant here" then I feel compelled to point out that an ontology is most certainly envisioned -- wikidata is implementing the SMW Property namespace! Undoubtedly it will use Category: for owl:Class representations, just like SMW. And builtin Datatypes, just like SMW. So, wikidata actually is *100%* concerned with the semantic web.
Then your discussion turns to templates: "Centralizing infobox designs is a good idea ... But neither (styling nor templates) is or should be put in relation with wikidata." Sorry but this unsupported assertion is irrelevant to whether wikipedias' requests to the wikidata server are for rdf triples or for html/a objects.
Finally you note that "This sounds like one of the many things a template repository wiki will be doing. But wikidata is not a template repository and is explicitly designed to disallow anything even like it." Apart from whether wikidata can play the role of a [http://www.mediawiki.org/wiki/Template_repository] with regard to Infobox templates is totally beside the point here as the issue now is about what is being retrieved from wikidata -- is it rdf triples or html/a objects.
In the former case, wikidata is the de facto designated hub for the entire constellation of wikipedias. In the other, each wikipedia is a source of reusable, annotated information, with a distinct possibility of retrieving information beyond the infobox from within the body of the article.
I've earlier sketched the scenario of an author on a wikipedia who would log into wikidata, build an infobox for a topic, save it, and then transclude its page. Obviously wikidata will at some point provide that author a list of available templates -- **keyed by the type of topic named by the author**. So yes I think wikidata will over time naturally play the role of a language-sensitive repository of infobox templates (and queries and maps and charts and so forth - see [[mw:extension:semantic result format]].
Thanks - john