Using ?module= is actually done throughout matomo. This seems more like a server configuration issue to me? Given matomo requests should almost always go to index.php by default.

While I agree that this is a server configuration issue, I didn't see any other Matomo requests that don't use index.php in the URL.
Both URLs linked to like index.php?module=CoreAdminHome&action=home and API requests like index.php?date=today&module=UserCountryMap always seem to include the index.php part in the URL.

Those, I'm guessing, go through a single code path (ie, piwik-api.js) so would be uniform. I'm sure there are links in matomo, however, that link to ?.... I guess we can still change this one though.