There is one important reason why we use <link> instead of <style>…</style>: when the rendered page HTML is cached, e.g. using a caching proxy like Varnish [1] or MediaWiki file cache [2], then if we used <style>…</style>, you would have to purge every page on the wiki before changes to MediaWiki:Common.css would actually take effect, because the CSS would be embedded in the cached HTML.
Using <link> means that it only takes as long as it takes the cached resource to expire in the users' browsers. (By default, they are set to expire after 5 minutes.)
If you don't have caching enabled, then of course that wouldn't matter – but also, if you don't have caching enabled, then that is probably a much worse performance problem than not embedding the styles :)
[1] https://www.mediawiki.org/wiki/Manual:Varnish_caching [2] https://www.mediawiki.org/wiki/Manual:File_cache