E.g. I go to the Hungarian Wikipedia, use Citoid to insert a link to a Hungarian newspaper, Citoid adds a languge=hu parameter. That does not seem helpful.

On one hand, the template should probably be intelligent enough to not display it, and having it helps to differentiate from cites where the language could not be detected, or the user created the template manually and did not bother to fill in the language (in both cases it might actually be in non-contentlang). On the other, citations are already a major wikitext usability problem so it's probably bad to add any unnecessary arguments to them.