From the linked article and FAQ, it sounds like this was once meant to be a differentiator, but the Voting Rights Policy mentioned in that SEC document is no longer a rule of the exchange, and tenured voting rights are not a listing requirement. Also not clear if other exchanges would disallow such voting rights.

Besides the complications this would raise that you mentioned, I also wonder how companies would even track tenure of ownership, since many (most?) shares of stock are not directly held and so the company may not even know who the nominal shareholder is or when transfers take place.