You still need driver ICs, but they are already integrated into the LEDs. So the PCB gets simpler but you have one controller per LED, so with 36 LEDs you‘re paying for 36 controllers.
“Tons of shift registers“ is exaggerated. Microcontrollers like the ATtiny88 already have 28 GPIOs, so up to 26 or so you wouldn‘t need any shift registers. If you opt for a small controller plus shift registers, it still would only be 1/8 or 1/16 of the number of LEDs, which isn’t tons. You‘re right about the resistors, but with industrial PCBA that shouldn’t be an issue.
Your pre-connected break-away approach is awesome and makes it very versatile.
And it‘s great to see a finished project. That thread on the german forum has been there for years, received many replies but nobody has shown working hardware before.