As I interpret your question, you want eighty 700 mA LEDs each with their own dimmer.
This is likely the most challenging LED project I have seen.
What is the target size for the PCB?
What is the part number of the LEDs?
You must use a switching CC regulator, a linear PWM register driver will not work at 80 x 700 mA. Even with a switcher an 80% efficient driver would not be easy.
With strings of LEDs 97% efficiency is easy.
With a single LED (highlighted) 80%, not so easy.
For $12 each ($3 / LED) this Linear Tech LT3476 quad LED driver may work for you.
Otherwise your PCA9632, or a shift register driver with multiple PWM outputs (e.g. TLC5917), driving the PWM inputs of 80 individual 700 mA drivers is the only viable option.
Replace LEDs with resistors and use as PWM generator.
If you could use multiple LEDs to reduce the 700 mA, that may open up additional alternatives.
Therefore I would like to use a voltage source with approx. 24V or
higher to transfer the power with thinner cables and somehow reduce
the 24V to 3.2V or so far that exactly 0.7A flows through the LED.
The power supply voltage would depend upon the Vf of the LEDs and the overhead voltage required by the LED drivers. I do not see the problem with the mains power being run to a 3.3V - 5V power supply near the PCB. I do not understand why you would suggest a 24V supply for a single strip. Would this be a multiple PCB or single PCB project? A 24V supply line could cause more problems than it solves.
Because you need a switching CC driver for each LED, the supply voltage does not need to be much above the LED's Vf. A supply of 24V will decrease efficiency. And you NEED efficiency. 5V should be more than sufficient for driver overhead and distribution drops.
Keeping the LEDs cool is a bigger problem than power distribution. But the solution for one can also work for the other.
You do not say what the length of the strip will be, but I would say it is very likely there will be a heatsink running the entire length of the strip. I usually used the heatsink as the ground buss.
Then one side of the PCB is solid copper heat spreader and also the 48V buss. The tracks connecting the LEDs are copper pours that are also used to spread heat. With 2 oz copper the track resistance is below 0.02Ω per foot.
a total current of up to 56A could occur which in many respects is
very impractical and hardly feasible.
It would be a challenging project. How feasible depends on the PCB size. I doubt it could be done with passive cooling if a single PCB.
The challenge is to use as much of the input power to generate photons rather than heat and then move the heat away from the LEDs as quickly as possible. The lateral heat transfer to move the heat away from the LEDs takes more than just PCB copper planes.
You will have a massive thermal management problem if you want these LED close to one another. 20 red = 15 W, 20 each GBW = 134 W = 150 W for the LEDs + the LED drivers. The power that needs to be dissipated PD would depend upon the efficacy of the LEDs. PD could be easily reduced to less than 75 W with quality LEDs. I would take a close look at Luxeon Color C Line for this project. I generally like OSRAM Oslon or Cree XPE for color LEDs. When looking at Luxeon Color C it is very important to know they are spec'd at 85°c. This makes a huge difference for red's efficiency. Luxeon Color C also has very good color mixing optics.
The problem color will be green. Green is the least efficient (in radiometric terms) LED with the highest Vf. You may not be able to find a green with a typical Vf below 3.2v. The Luxeon Color C green LED has a typical Vf of 2.55V, lower than all other high power green. Green is the reason a 3.3V supply is not viable. Keep in mind the 2.55V is at 85°C, to compare it to other LEDs spec'd at 25°C you need to add 144 mV (60° x 2.4 mV) to the Luxeon due to the coefficient of temperature.
High power green LEDs are the most problematic.
Running thermal experiments on 40 Watt strip of green.
This is a water cooled dual strip. The copper bar could be split in two, one half for ground and one half for VCC. They could be thermally reconnected with thermal tape as an electrical insulator.
You may be able to do a passive heatsink that runs cool enough to not burn up the LEDs then add a fan. This way if the fan fails, the LEDs are not ruined.
I have found that mounting a thin (0.062") copper or aluminum strip to the LED side of the board does better than using thermal vias. In small quantity I pay about $1 per foot for a 0.5" wide copper bar.
The strip below has a single high power LED spaced 0.7" apart. Thermal management was difficult. Red LEDs are very thermal sensitive as they will easily lose 50% of their radiant flux due to temperatures that are otherwise acceptable for white and blue. If the electrical watts are not radiated as photons, they must be dissipated as heat. You don't need more heat.
Even if your LEDs were spaced far enough apart you'd still have 4 times the thermal management issues as this water cooled strip.
To quickly move the heat away from high power LEDs I found it requires the copper bar to be mounted, directly to, and as close as possible to the LED's thermal pad on the component side of the PCB.
If you mount your LEDs in squares of 4 LEDs you will need a copper bar on each side of the LEDs. If you use one copper bar for GND and the other for VCC, you no longer have a power distribution problem.
The PCB footprint for four (RGBW) Luxeon Color C
I find this much better solution than using an LED Engin LZ4 RGBW
LED size is 1.8 mm x 1.8 mm
Screw hole (gold circle) 3.3 mm dia.