Mark Zuckerberg’s grand plan to combine Facebook Messenger, WhatsApp, and Instagram into one gigantic iMessage-rivaling chat service might soon be met with more than skepticism by the industry’s regulatory authorities around the world.

One such agency, called the Bundeskartellamt, or the Federal Cartel Office, has already taken issue with Facebook’s intrusive practices of combining user data from different sources. These will obviously only get worse if the social networking giant does end up merging its three flagship products, although users are likely to be better informed of what sort ...