On Sat, 13 Jan 2018, at 9:21 AM, John Lewis wrote:
Help:Templates says that there is no central repository for templates. Is there a technical reason for that?
No technical reason against such a thing, I think, so much as that templates are very often quite site-specific and tied in to things like specific skins, site CSS or JS, and bureaucratic processes on particular wikis.
That said, you can grab a template from any MediaWiki wiki out there via the Special:Export page. This has a "Include templates" checkbox, that will make it download not only the template that you request but also all of the templates and modules on which it depends. (It won't get associated pages in other namespaces though, unless you list those explicitly.)