The desktop version absolutely does not have that requirement, you just have to buy the right one. Office 2016 can be installed and used offline without ever talking to a Microsoft server. You're referring to a restriction specific to the Office365 version. If you don't want cloud requirements, don't buy the cloudy version.

You know, "buying the right one" Microsoft product can easily be a full time job. That is, if it is even possible. I was under the impression that the only version of Office available was the 365.

But anyway, my workplace brought some version with a clear requirement of getting an eternal license on it. Yet, it breaks all the time because it can't get licenses on the cloud. I am still not sure how MS isn't evading the requirements, but well, it's not my job to check it.

Curious, when I Google "Microsoft Office" the first non-ad response is literally the page explaining which version is which and how much they cost.