Perhaps I'm not getting my point across as clearly as I'd like. I'm not saying this isn't a big change, because it is. What I'm trying to say is that it's a big change that doesn't add much to the game and instead serves to make it more cumbersome.
By their wording, all envoy yields are now going to be tied to this one district. Now, in the metagame in Civ VI as it stands, there's going to be three districts you have in all your cities: Campus, Theater Square, and Commercial Hub/Harbor. Maybe if you're playing a Dom or Religion game, you get a Holy Site or Encampment as a replacement for one of those. Assuming you have a city with 10 pop, which is a reasonable estimate for the mid-game in Civ VI, you can fit four districts in it. Early on, you'll probably only have room for three (7 pop). You'll also need to find room for Industrial Zones in some of those cities, and one of your cities you'll also need to make room for the Government Plaza.
Do you see the problem here? It's not just that all of those yields are getting moved to the Diplomatic Quarter, it's that the Diplomatic Quarter itself will be a massive opportunity cost for one of your core districts. The previous system was far more elegant in its execution: the yields were tied to the associated district. If you wanna befriend a bunch of scientific City States, you just need to have Campuses (which you already will, because you're playing a scientific game). Now, to reap the benefits of those City-States, you have to spend part of your District cap in your cities on a Diplomatic Quarter.