Unfortunately, touching the lighting engine is a large part of what makes Cubic Chunks so difficult to implement. Doing proper lighting in Minecraft is neither easy nor cheap (system resource wise).
The problem with inheriting light levels from chunks above you in a theoretically infinite height world is that the chunks above you have never been generated in the first place. Take the following thought example:
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Actually it is solveable - by doing lighting differently. Currently the MC lighting system relies on having a "connection to the sky" but with an infinitely tall world, you cant really tell where the sky will be.
So to fix, you split the lighting up into different types: Torchlight and Sunlight. With appropriate generators for both. Torchlight is well understood. there are a LOT of existing mods to generate light. A Sunlight generator is something new, but we are all familiar how mobs (and mods) react to sunlight. the only change is how to generate it. Your massive underground cave can have a sunlight generator somewhere. Or you can define something that says "if you have more than XXX unbroken air, you get sunlight" -- but this could be very exploitable, im sure somebody can come up with a better way.
Gameplay wise, the main issue with an infinite vertical would probably be the distribution of resources. The game is designed so you can get iron fairly quickly, and it doesn't take too long to make it to the depths and get your diamonds. For me it would feel funny having the depth go down thousands of metres while you only have to dig down about 60 to get to the most valuable resources in the game. Most likely it would work best with some kind of mod that changes the vanilla progression and adds more types of resources and challenges for those who want to dig deeper. Of course if it was implemented in Vanilla they'd have to overhaul the entire resource progression. Another recommendation would be lifting the artificial speed cap on vanilla minecarts so they can keep accelerating as long as you're going downhill (or are getting boosted), only limited by friction and resistance. Being able to build an elevator shaft would be nice as well (a "vanilla" version could simply have the motor consume coal in its inventory to run). Currently I will consider just the overworld and neglect the Nether for the time being
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Now as to the problem with ore generation. The current system says 'spawn diamonds between y=1 and y=12' and 'spawn gold between y=10 and y=30' (or something close). But they are all ABSOLUTE values. if y goes to -35,000 then when you go below y=1, diamonds stop spawning. Now you could change it slightly "spawn diamonds below y=12" Which will work, but as others have pointed out, if you setup a quarry to mine all the way down, then you get way too many resources.
So again - you change the way things currently work. Instead of absolute values, you go with a percentage. Now this assumes your world has a preset max depth and max height, and it doesnt change after world creation.
If we convert the values for diamonds and gold into percentages, we get: "spawn diamonds between 1% and 12%" and "spawn gold between 10% and 30%"
So if your world is 1,000 blocks tall (-500 to +500) diamonds will spawn between -490 and -380, and gold will spawn between -400 and -200
And if you want vanilla, your world will be 128 blocks tall (yes i know you can build up to y=256). So diamonds will spawn between 0 and 15, and gold will spawn between 12 and 38.
For the 1k block tall world, having nearly 100 blocks of diamond spawning sounds excessive.. but ponder what it will take to dig down to y=-380 from y=0?.. Starting at y=0 thats 380 blocks. Starting at y=64 thats 444 blocks. The first one is nearly 1.5x as tall as what minecraft currently allows. the 2nd one is nearly TWICE as tall as anything currently possible. a HUGE amount of digging. Completely doable with automation and mods. But in vanilla? your going to be a while.