I don't think a city needs multiple districts of the same type to further specialise. A district isn't completed with just constructing it itself. There are up to 4 buildings in it that also need constructing.
So a city that really really specialices in science is not one with 3 science districts but one with a fully developed one.
A city with just district+library just does the neccesary thing to generate a few beakers.
If you think in CiV terms, not every one of your cities probably had a science lab or a museum.
So if you want to really specialise in science or culture output you will have to research the upgrade buildings and not just plaster the land with multiple districts.
But once those buildings are unlocked, they will be built in every science district (if science is still as OP as it seems).
And every city did build the science lab or museum eventually, (some were slow..which means they never got to that "level of development" but once the city was at a certain "level of development" it had all of the buildings for that... only a very few buildings really specialized the city..ie XP, Defense, and some buildings that you rushed earlier in cities because they were already specialized.)
(also if science is as OP as it seems, then the tech tree will be imbalanced as you point out, and everyone at X tech will have science buildings)
Also if the tech is as tightly interconnected as in CivV, then at era X everyone will have certain sets of buildings.
That is actually what I am saying too. If a small island city is able to build multiple harbour districts on the coast tiles...

wait a minute, maybe it is not a good idea after all. To have say 3 lighthouses would make a resourceless sea tile to give like 4 food (assuming it will still have a similar ability). No that would be too overpowered. Since other buildings will have similar ability giving certain tiles or resources extra yield, this would not be fun.
Any buildings that give +% yield would have to have that effect be non repeatable
Buildings that gave + per pop or per tile could work, as long as there are balanced competing buildings in other districts
(If a lighthouse gives +1 food to sea tiles, then a workshop should give +1 production to land tiles.... And everything would be 10x more expensive)
But if a Lighthouse were designed to be in a repeatable Harbor district it might be something like
CAN work sea tiles without resources (sea tiles with resources workable by default), +1 food per sea tile adjacent to this district, +1 gold per sea resource adjacent to this district