I am actually really excited about the diplomatic district, and I think it will indirectly buff tall gameplay.
This is theorycrafting, but I think the way DD will work in practice is that it will make the envoy game inaccessible to playstyles focused on spamming settlers or units for conquest. Basically, when I focus on playing tall early game, I find myself getting to luxuries like gov't plaza and other less critical districts a lot earlier. So I imagine that I'll naturally get the diplo district. This in turn will allow tall civs to buff their buildings via city states much more effectively than wide civs, as I have always felt that city state building bonuses are the best way to improve yields from districts.
The counter-argument is that wide empires will have more space and more cities with which to commit to the DD. I hope in order to prevent this that they make the DD a bit too pricey to have a tier 2 or tier 3 city commit to.