As far as this general concept goes, I have to say I like it. Hear me out!
It doesn't prevent wide. You don't need districts for a city to be valuable. Cities can still grab strategic resources, new luxes to help your core cities, 'old' luxes to allow more wide cities, production for military, terrain for pantheon or other unique bonuses or unique improvements, grabbing terrain for strategic reasons, terrain for dig sites, terrain to limit growth of opponents and to make the march toward your core cities more difficult for enemies, etc, etc. I might be forgetting something else pop could be good for.
It does mean that we will likely have some handful of cities 2-5? which are much better, taller, "districted" cities. These will be the core cities of empires. They won't be the only tall cities, since you can have farms anywhere, but they will be the only highly developed tall cities. Or perhaps it will be possible to go wide and specialize districts, placing 1-2 in each city only.
On top of that, civs with unique (plus Germany's 1 'free' district) will be able to have those districts in their wide cities, but they will have to go about it strategically. I'm not opposed to the idea of some civs having better or more specialized wide empires, as long as it's balanced out in the end.
I think the crux will be if new cities or city centers end up contributing to the inflation. If they don't, then you can go wide to your heart's content, and then start putting down whatever districts you want to have in your wide cities. If they do, then probably the best way to have a unique district in every city will be to settle a city, build the district, rinse and repeat. Each city's UD will be more expensive.